Physics SME

  Key Unit Competence: 

Analyse the effects of sound waves in elastic medium

Introductory activity

What are the properties which explain mostly the behavior of sound?

1. a) Most people like to listen to music, but hardly anyone likes to listen 
           to noise. In your own view, how is musical sound different from noise?
    b) A guitarist as shown in the figure above plays guitar. The sound is 
       made by the vibration of the guitar string and propagates as a wave 

        through the air and reaches your ear. 

i) Assuming you are near by the guitarist and your friend is behind you, 
     who can hear more sound? Explain your reasoning
ii) If another person playing flute comes in and plays it. Can you distinguish 
    sound from the flute from that of a guitar? How are the two sounds 

      different?

2. a) Now, while they are playing their instruments you keep moving away 
       and coming towards a point where they are playing the instruments. 
       Explain the variations of sound heard by you.
    b) Do you think there would be any change in the sound if you(the 
      observer) and the players (the source) remained in the same position?
3. With scientific explanations explain why you may not be able to 

     communicate well in a room where music is being played at a high tone.

1.1 PRODUCTION OF STATIONARY SOUND WAVES

           Activity 1.1

   Look at the Fig.1.2 and then answer the following questions.

         

1. The two students in the figure above are producing sound. In each case, 
      describe the method of production of sound.
2. Imagine that the student replaces the flute with a longer one, would the 
    sound produced remain the same?Explain you answer.
3. Do you think a guitar with longer string produces the same sound as 
    the one with a shorter string? Defend your answer using scientific 

     explanations.

         1.1.1 Sound in pipes

The source of any sound is vibrating object. Almost any object can vibrate and hence 
be a source of sound. For musical instruments, the source is set into vibration by 
striking, plucking, bowing, or blowing. Standing waves (also known as stationary 
waves are superposition of two waves moving in opposite directions, each having 
the same amplitude and frequency) are produced and the source vibrates at its 
natural resonant frequencies. The most widely used instruments that produce 
sound waves make use of vibrating strings, such as the violin, guitar, and piano or 
make use of vibrating columns of air, such as the flute, trumpet, and pipe organ. 
They are called wind instruments.

We can create a standing wave:
• In a tube, which is open on both ends. The open end of a tube is approximately 
a node in the pressure (or an antinode in the longitudinal displacement). 
• In a tube, which is open on one end and closed on the other end. The closed 
end of a tube is an antinode in the pressure (or a node in the longitudinal 
displacement).

In both cases a pressure node is always a displacement antinode and vice versa.

A node is a point half way between the crest and the trough. The line that connects 
the nodes is the nodal line. The nodal line shows the original position of the matter 
carrying the wave.

Displacement node means that a very thin slice of the medium at the node does 
not move (zero displacement). If you have a standing wave in a half-open tube, 
there will be a displacement node (and a pressure antinode) at the closed end. 
This is due to the fact that the molecules cannot move back and forth at the closed 
end.In the open end you will, on the other hand, have a pressure node (and thus a 
displacement antinode). This is due to the fact that the pressure at the end of the 

tube is equal to that of the surrounding air.

Pressure node does not mean that the pressure is low; it simply means that the 
pressure is constant. Similarly, the pressure at the antinode is not “high”; it simply 

has the largest oscillations from low pressure to high pressure.

a. Tube of length L with two open ends

An open pipe is one which is open at both ends. The length of the pipe is the 

distance between consecutive antinodes. But the distance between consecutive 

        

The longest standing wave in a tube of length L with two open ends has displacement 

antinodes (pressure nodes) at both ends. It is called the fundamental.

          

Notes with higher frequencies than fundamental can be obtained from the pipe by 
blowing harder. The stationary wave in the open pipe has always an antinode at 
each end.
The next longest standing wave in a tube of length L with two open ends is the 
second harmonic (first overtone). It also has displacement antinodes at each 

end.

                

                  The second overtone is obtained from Fig. 1.6 and is the third harmonic. 

Example 1.1

b. Tube of length L with one open end and one closed end.

The longest wavelength of standing wave in a tube of length L with one open 
end and one closed end has a displacement antinode at the open end and a 

displacement node at the closed end. This is the fundamental.

                       

             

The next longest standing wave in a tube of length in a tube of length L with one 
open end and one closed end is the third harmonic (second overtone). It also 

has a displacement antinode at one end and a node at the other.

               

       An odd-integer number of quarter wavelength has to fit into the tube of length L.

                    

          frequencies. Only odd harmonics of the fundamental are natural frequencies. 

Example 1.2

A section of drainage culvert 1.23 m in length and makes a howling noise when 
the wind blows. 
a. Determine the frequencies of the first three harmonics of the culvert if it is 
      open at both ends. Take v = 343 m/s as the speed of sound in air. 
b. What are the three lowest natural frequencies of the culvert if it is blocked 
     at one end?
c. For the culvert open at both ends, how many of the harmonics present fall 

     within the normal human hearing range (20 Hz to 17 000 Hz)?

      

      1.1.2 Vibrating strings

The string is a tightly stretched wire or length of gut. When it is struck, bowed or 
plucked, progressive transverse waves travel to both ends, which are fixed, where 
they are reflected to meet the incident waves. A stationary wave pattern is formed 
for waves whose wavelengths fit into the length of the string, i.e. resonance occurs.

If you shake one end of a cord (slinky) and the other end is kept fixed, a continuous 
wave will travel down to the fixed end and be reflected back, inverted. The 
frequencies at which standing waves are produced are the natural frequencies 
or resonant frequencies of the cord. A progressive sound wave (i.e. a longitudinal 
wave) is produced in the surrounding air with frequency equal to that of the 
stationary transverse wave on the string.

Now let consider a cord stretched between two supports that is plucked like a 
guitar or violin string. Waves of a great variety of frequencies will travel in both 
directions along the string, will be reflected at the ends, and will be travel back in 
the opposite direction. The ends of the string, since they are fixed, will be nodes.

Consider a string of length L fixed at both ends, as shown in Fig.1.10. Standing 
waves are set up in the string by a continuous superposition of wave incident on 
and reflected from the ends.
 
Note that there is a boundary condition for the waves on the string. The ends of the 
string, because they are fixed, must necessarily have zero displacement and are, 

therefore, nodes by definition.

                   

Fig.1. 10 (a) A string of length L fixed at both ends. The normal modes of vibration form a harmonic 
series: (b) the fundamental note; (c) First overtone; (d) the second overtone (Halliday, Resneck, & 

Walker, 2007).

 Example 1.3

A piano string is 1.10 m long and has mass of 9 g. 
     a. How much tension must the string be under, if it is to vibrate at a fundamental 
          frequency of 131 Hz?

    b. What are the frequencies of the first four harmonics?

        

Resonance of sound

We have seen that a system such as a taut string is capable of oscillating in one or 
more normal modes of oscillation. If a periodic force is applied to such a system, 
the amplitude of the resulting motion is greater than normal when the frequency 
of the applied force is equal to or nearly equal to one of the natural frequencies 
of the system. This phenomenon is known as resonance. Although a block–
spring system or a simple pendulum has only one natural frequency, standing-wave 
systems can have a whole set of natural frequencies. 

Because oscillating systems exhibit large amplitude when driven at any of its natural 
frequencies, these frequencies are often referred to as resonance frequencies. 
Fig.1.11shows the response of an oscillating system to various driving frequencies, 
where one of the resonance frequencies of the system is denoted by 
  
                                         
Fig.1. 11: Graph of the amplitude versus driving frequency for oscillating system. The amplitude is 
a maximum at the resonance frequency. Note that the curve is not symmetric (Halliday, Resneck, & 

Walker, 2007)

A more spectacular example is a singer breaking a wine glass with her amplified 
voice. A good-quality wine glass has normal-mode frequencies that you can hear 
by tapping it.

If the singer emits a loud note with a frequency corresponding exactly to one of 
these normal-mode frequencies, large-amplitude oscillations can build up and 

break the glass (Fig. 1.12) 

                               

             

Fig.1. 12 : Some singers can shatter a wine glass by maintaining a certain frequency of their voice 
for seconds, (a) Standing-wave pattern in a vibrating wine glass. (b) A wine glass shattered by the 

amplified sound of a human voice

  Beats and its phenomena

Beats occur when two sounds-say, two tuning forks- have nearly, but not exactly, 
the same frequencies interfere with each other. A crest may meet a trough at 
one instant in time resulting in destructive interference. However, at later time the 
crest may meet a crest at the same point resulting in constructive interference. To 
see how beats arise, consider two sound waves of equalamplitudes and slightly 

different frequencies as shown on the figure below.                

             

Fig.1. 13: Beats occur as a result of the superposition of two sound waves of slightly different 

frequencies (Cutnell & Johnson, 2006).

In 1.00 s, the first source makes 50 vibrations whereas the second makes 60. We 
now examine the waves at one point in space equidistant from the two sources. 
The waveforms for each wave as a function of time, at a fixed position, are shown 
on the top graph of Fig. 1.13; the red line represents the 50 Hz wave, and the blue 
line represents the 60 Hz wave. The lower graph in Fig. 1.13 shows the sum of 
the two waves as a function of time. At the time the two waves are in phase they 
interfere constructively and at other time the two waves are completely out of phase 
and interfere destructively. Thus, the resultant amplitude is large every 0.10 s and 
drops periodically in between. This rising and falling of the intensity is what is heard 
as beats. In this case the beats are 0.10 s apart. The beat frequency is equal to 

the difference in frequencies of the two interfering waves.

       

The interference pattern varies in such a way that a listener hears an alternation 
between loudness and softness. The variation from soft to loud and back to soft 
is called a Beat. The phenomena of beats can be used to measure the unknown 

frequency of a note.

       

Application activity 1.1

1. Is the wavelength of the fundamental standing wave in a tube open 
    at both ends greater than, equal to, or less than the wavelength of 
    the fundamental standing wave in a tube with one open end and one 
    closed end? Explain your answer.

2. You blow across the opening of a bottle to produce a sound. What 
     must be the approximate height of the bottle for the fundamental note 
     to be a middle C (with the wavelength of 1.29 m).

3. Two loudspeakers are separated by 2.5 m. A person stands at 3.0 m 
    from one and at 3.5 m from the other one. Assume a sound velocity of 
    343 m/s.

a. What is the minimum frequency to present destructive interference at 
     this point?
b. Calculate the other two frequencies that also produce destructive 
     interference.
4. How would you create a longitudinal wave in a stretched spring? Would 
    it be possible to create a transverse wave in that spring?

5. In mechanics, massless strings are often assumed. Why is this not a 
    good assumption when discussing waves on strings? 

6. Draw the second harmonic (The second lowest tone it can make.) of 
     a one end fixed, one end open pipe. Calculate the frequency of this 
     mode if thepipe is 53.2 cm long, and the speed of sound in the pipe is 
      317 m/s.
7. Calculate the wavelengths below. The length given is the length of the 

      waveform in the picture bellow:

          

8. A guitar string is 64 cm long and has a fundamental Mi frequency of 
     330 Hz. When pressing in the first fret (nearest to the tuning keys) see 
     figure bellow the string is shortened in such a way that it plays a Fa 
     note having a frequency of 350 Hz. Calculate the distance between 

     this first fret and the nut necessary to get this effect. 

                        

9. Why is a pulse on a string considered to be transverse?
10. A guitar string has a total length of 90 cm and a mass of 3.6 g. From 
      the bridge to the nut there is a distance of 60 cm and the string has 
      a tension of 520 N. Calculate the fundamental frequency and the first 

      two overtones

1.2 CHARACTERISTICS AND PROPERTIES OF SOUND WAVES

    Activity 1.2

  Read the scenario below and answer the questions that follow.
On an interview for Physics placement in a certain school in Rwanda, Claudette 
a S.6 leaver who had applied for the job was asked about sound waves
during the interview.

She was asked to state the properties of sound waves. Confidently, she 
responded that the properties are reflection, refraction, diffraction and
interference. This was enough to make Claudette pass the first level of the 
interview.

However, in the second step, she was required to discuss different media 
in which sound waves can propagate. Claudette started discussing these 
different media. What surprised the interviewer was Claudette’s ability to relate 
sound waves to other kinds of waves stating that these waves behave the 

same way when they pass from one medium to another.

Looking at Claudette’s face, the interviewer asked her to discuss the laws 
governing reflection and refraction of sound waves. With a smile, she 
started by saying that since sound waves have the same properties as for light; 
these laws therefore do not change.

As she was attempting to state them, the interviewer stopped her and 
congratulated her upon her confidence and bravery she showed in the room. 
She was directly told that she was successful and she was given the job. 
Claudette is now working as assistant S2 Physics Tutor and doubles as a 
Physics laboratory attendant.

Questions
      a. Explain the meaning of underlined terms used in the text above?
      b. Do you think, it was 100% correct for Claudette to relate sound waves 
            to light waves? Explain?
     c. There is where she was asked to discuss the different media in which 
           sound waves can propagate. Discuss these different media and talk 
          about speed of sound waves in the stated media.
     d. In one of the paragraphs, Claudette said that the laws governing reflection 
        and refraction of sound waves were similar to those of light. Can you 
        explain these laws (Use diagrams where possible)
    e. Assuming that you were an interviewer and the interview was out of 80. 

         What mark would you award to Claudette? Why?

        1.2.1 Properties of sound waves

Most of us start our lives by producing sound waves! We spend much of our life 
surrounded by objects which produce sound waves. Most machines in use vibrate 
and produce sound so the only sure way to silence them would be to put them in 
vacuum where there would be no surrounding medium for the vibrating surfaces 
of the machine to push against, hence no sound waves. Some physiologists 
are concerned with how speech is produced, how speech impairment might be 
corrected, how hearing loss can be alleviated. 

Sound is associated with our sense of hearing and, therefore, with the physiology 
of our ears that intercept the sound and the psychology of our brain which interprets 
the sensations that reach our ears. Sound waves are longitudinal mechanical waves 
that can travel through solids, liquids, or gases.

As the sound wave propagates, many interactions can occur, including reflection, 
refraction, diffraction and interference. When a sound wave hits a surface, a part of 

the energy gets scattered while a part of it is absorbed. 

a. Reflection of sound wave

    Fixed end

First consider an elastic rope stretched from end to end. One end will be securely 
attached to a pole on a lab bench while the other end will be held in the hand in 
order to introduce pulses (single disturbance, on vibration) into the medium as 
shown in Fig.1.14. Because the right end of the rope is attached to a pole (which is 
attached to a lab bench), the last particle of the rope will be unable to move when 

a disturbance reaches it. This end of the rope is referred to as a fixed end.

                

                      Fig.1. 14 An elastic securely tied to a pole can be used to study the behavior 

                     of waves at a fixed end

If a pulse is introduced at the left end of the rope, it will travel through the rope 
towards the right end of the medium. This pulse is called the incident pulse since 
it is incident towards (i.e., approaching) the boundary with the pole. 

When the incident pulse reaches the boundary, two things occur:

• A portion of the energy carried by the pulse is reflected and returns towards 
  the left end of the rope. The disturbance that returns to the left after bouncing 
  off the pole is known as the reflected pulse.
• A portion of the energy carried by the pulse is transmitted to the pole, causing 
  the pole to vibrate.

When one observes the reflected pulse off the fixed end, there are several notable 
observations. First the reflected pulse is inverted. That is, if an upward displaced 
pulse is incident towards a fixed end boundary, it will reflect and return as a 

downward displaced pulse. 

                  

                  Similarly, if a downward displaced pulse is incident towards

                   a fixed end boundary, 

it will reflect and return as an upward displaced pulse.

The inversion of the reflected pulse can be explained by returning to our conceptions 
of the nature of a mechanical wave. When a crest reaches the end of a medium 
(“medium A”), the last particle of the medium A receives an upward displacement. 
This particle is attached to the first particle of the other medium (“medium B”) on 
the other side of the boundary. As the last particle of medium A pulls upwards on 
the first particle of medium B, the first particle of medium B pulls downwards on the 
last particle of medium A. 

In general, Reflection leaves wavelength, speed, amplitude and frequency 

unchanged.

Free End Reflection

Suppose a rope is attached to a ring that is loosely fit around the pole as in Fig.1.16. 
Because the right end of the rope is no longer secured to the pole, the last particle 
of the rope will be able to move when a disturbance reaches it. This end of the rope 

is referred to as a free end.

                                            

Fig.1. 16 If the end of elastic rope not fastened to the pole then it will befree

 to move up and down. This provides for the study of wave behavior at free end

When an upward displaced pulse is incident upon a free end, it returns as an 
upward displaced pulse after reflection. And when a downward displaced pulse is 
incident upon a free end, it returns as a downward displaced pulse after reflection 

as in Fig.1.17. Inversion is not observed in free end reflection.

                       

 The reflection of sound waves can end up with any of the two phenomena either 
an echo or reverberation:
• Echo occurs when a reflected sound wave reaches the ear 0.1 s after we 
   hear the original sound. If the time elapsed between the arrivals of the two 
   sound waves is more than 0.1 s, then the sensation of the first sound will get 
   died out. An echo sounder or fathometer is a device used on a ship for the 

   purpose of measuring the depth of the sea.

In a small room the sound is also heard more than once, but the time differences 

are so small that the sound just seems to loom. This is known as reverberation. 

b. Refraction and Snell’s law and waves

Refraction of waves is the change in direction of waves as they pass from one 
medium to another. The bending of waves is accompanied by the change in speed 
and wavelength of the wave. So, if there is any change in media, the wave speed 
changes. Sound waves travel with less velocity in cool air than they do in the warmer 
air. 

When a wave travels from deep water to shallow water in such a way that it meets 
the boundary between the two depths straight on, no change in direction occurs. 
On the other hand, if a wave meets the boundary at an angle, the direction of travel 

does change. This phenomenon is called refraction (Fig.1.18)

        

                

Snell’s law (also known as Snell–Descartes law or the law of refraction) is 
a formula used to describe the relationship between the angles of incidence
and refraction, when referring to light or other waves passing through a boundary 
between two different isotropic media, such as water, glass, or air.

Snell’s law states that the ratio of the sines of the angles of incidence and refraction 
is equivalent to the ratio of phase velocities in the two media, or equivalent to the 

reciprocal of the ratio of the indices of refraction:

                                                  

Where

         

Comparisons between the characteristics of the transmitted pulse and the reflected 
pulse lead to the following observations.
• The transmitted pulse (in the less dense medium) is traveling faster than the 
   reflected pulse (in the denser medium).
• The transmitted pulse (in the less dense medium) has a larger wavelength 
   than the reflected pulse (in the denser medium).
• The speed and the wavelength of the reflected pulse are the same as the 

   speed and the wavelength of the incident pulse.

                  

Because this is less than the incident angle of 30°, the refracted ray is bent 
toward the normal, as expected. Its change in direction is called the angle 

of deviation and is given by

                            

c. Diffraction

Diffraction is the name given to the phenomenon in which a wave spreads out as 
it passes through a small aperture or around an obstacle. Diffraction patterns are 
formed when the diffracted waves interfere with one another to produce light and 
dark bands on a screen or piece of film. Diffraction patterns are most intense when 
the size of the aperture or obstacle is comparable to the size of the wavelength of 
the wave. Similar effects are observed when light waves travel through a medium 
with a varying refractive index. Diffraction is due to the wave nature of light

When light passes through an opening it is observed to spread out. This is known 

as diffraction and becomes more pronounced with narrower openings.

              

Diffraction occurs with all waves, including sound waves, water waves, and 
electromagnetic waves such as visible light, x-rays and radio waves. Since diffraction 
occurs for waves, but not for particles, it can serve as one means for distinguishing 

the nature of light.

d. Interference and principle of Superposition

Interference occurs when two or more waves traveling through the same medium 
overlap and combine together. Interference of incident and reflected waves is 

essential to the production of resonant standing waves.

We can have constructive and destructive interference:

• If a person stands equidistant from two speakers which are playing the same 
sound in phase, i.e. which are moving in and out together, then the two waves 
arrive in phase after traveling the same distance. Crest meets crest and 
trough meets trough at the location of the person. The amplitudes of the two 
waves add and the sound is loudest here.
• If the two speakers play the same sound but are out of phase, i.e. one is 
moving out while the other is moving in, and then the sound has a low volume 
at the location of the person equidistant from the two speakers. This can 
easily be demonstrated by switching the wires on one of the speakers. (This 
is why you need to pay attention to the color of the wires when setting up your 
stereo). Dead spots in an auditorium are sometimes produced by destructive 
interference.
In general, the term “interference” refers to what happens when two or 
more waves pass through the same region at the same time.

 The principle of superposition

Combining the displacements of the separate pulses at each point to obtain the 
actual displacement is an example of the principle of superposition: “When 
two waves overlap, the actual displacement of any point on the string at any time 
is obtained by adding the displacement the point would have if only the first wave 
were present and the displacement it would have if only the second wave were 

present”. 

Combining the displacements of the separate pulses at each point to obtain the 
actual displacement is an example of the principle of superposition: “When 
two waves overlap, the actual displacement of any point on the string at any time 
is obtained by adding the displacement the point would have if only the first wave 
were present and the displacement it would have if only the second wave were 

present”. 

In other words, the wave function y(t, x) that describes the resulting motion in this 

situation is obtained by adding the two wave functions for the two separate waves:

     

As we saw with transverse waves, when two waves meet, they create a third wave 
that is a combination of the other two waves. This third wave is actually the sum of 
the two waves at the points where they meet. The two original waves are still there 
and will continue along their paths after passing through each other. After passing 

the third wave no longer exists.

              

1.2.2 Characteristics of sound waves

Usually, the characteristics used to describe waves are period, frequency, 
wavelength, and amplitude.

a. Frequency ranges
Any periodic motion has a frequency, which is the number of complete cycles in 
a second and a period which is the time used to complete one cycle. While the 
frequency is measured in Hertz (Hz), the period is measured in seconds (s). For a 
wave, the frequency is the number of wave cycles that pass a point in a second. A 
wave’s frequency equals the frequency of the vibrating source producing the wave.
Sound waves are classified into three categories that cover different frequency 
ranges:

• Audible sound 
Audible sound lies within the range of sensitivity of the human ear. They can 
be generated in a variety of ways, such as musical instruments, human voices, or 
loudspeakers. It is almost impossible to hear sounds outside the range of 20 Hz to
20 kHz. These are the limits of audibility for human beings but the range decreases 

with age.

Hearing is the perception of sound. The hearing mechanism involves some 
interesting physics. The sound wave that impinges upon our ear is a pressure wave. 
The ear is a transducer that converts sound waves into electrical nerve impulses 

in a manner much more sophisticated than, but analogous to, a microphone.

• Infrasonic waves 

Infrasonic waves have frequencies below the audible range. They are sound 
waves with frequencies that are below 20 Hz limit. 

Some animals such as elephants can use infrasonic waves to communicate 
effectively with each other, even when they are separated by many kilometers. Their 
large ears enable them to detect these low frequency sound waves which have 

relatively long wavelengths.

Young bat-eared fox and Rhinoceros (Fig.1.21) also use infrasonic as low as 5 Hz 

to call one another. They have ears adapted for the detection of very weak sounds.

        

A number of animals are sensitive to infrasonic frequencies. It is believed by many 
zoologists that this sensitivity in animals such as elephants may be helpful in 
providing them with early warning of earthquakes and weather disturbances. It has 
been suggested that the sensitivity of birds to infrasound aids their navigation and 
even affects their migration.

• Ultrasonic waves 
Ultrasonic waves have frequencies above the audible range. They are sound 
waves whose frequencies are higher than 20 KHz. You may have used a “silent” 
whistle to retrieve your dog. The ultrasonic sound emitted by that device is easily 
heard by dogs, although humans cannot detect it at all. Ultrasonic waves are also 

used in medical imaging.

Some marine mammals, such as dolphin, whales, and porpoises use sound waves 
to locate distant objects. In this process, called echolocation, a dolphin produces 
a rapid train of short sound pulses that travel through the water, bounce off distant 
objects, and reflect back to the dolphin. From these echoes, dolphins can determine 
the size, shape, speed, and distance of their potential prey. Experiments have 
shown that at distance of 114 m, a blindfolded dolphin can locate a stainless-steel 
sphere with a diameter of 7.5 cm and can distinguish between a sheet of aluminum 
and a sheet of copper. The Ultrasonic waves emitted by a dolphin enable it to see 

through bodies of other animals and people (Fig.1.22). 

            

Skin muscles and fat are almost transparent to dolphins, so they see only a thin 
outline of the body but the bones, teeth and gas-filled cavities are clearly apparent. 
Physical evidence of cancers, tumors, heat attacks, and even emotional shake can 
all be seen by dolphin. What is more interesting, the dolphin can reproduce the 
sonic signals that paint the mental image of its surroundings, and thus the dolphin 
probably communicates its experience to other dolphins. It needs no words or 
symbol for fish, for example, but communicates an image of the real thing.

Dogs, cats and mice can hear ultrasound frequencies up to 450 000 Hz. Some 
animals not only hear ultrasound but also use ultrasonic to see in dark. Bats also 
use echo to navigate through air. Bats use ultrasonic with frequencies up to 100 

000 Hz to move around and hunt (Fig.1.23). 

              

The waves reflect off objects and return the bat’s ears. The time it takes for the 
sound waves to return tells the bat how far it is from obstacles or prey. The bat uses 
the reflected sound waves to build up a picture of what lies ahead.

The process of imaging using Sonar (Sound Navigation and Ranging) is the same 
as the echo-locating sonar of a submarine or a bat. The observer sends out a brief 
pulse of ultrasound and waits for an echo. The pulse travels out, reflects off the 
target and returns. The ultrasound machine uses pulses because the same device 
acts as both transmitter and receiver.


Ultrasound has been used in a variety of clinical settings, including obstetrics and 
gynecology, cardiology and cancer detection. The main advantage of ultrasound 
is that certain structures can be observed without using radiation. Ultrasound can 
also be done much faster than X-rays or other radiographic techniques.

Ultrasonic waves can be used to produce images of objects inside the body thus 
Physicians use ultrasonic to observe fetuses. Ultrasound has frequencies too high 
for you to hear. Echoes from ultrasound waves can show what is inside the body. 

Echo is a reflection of sound off the surface of an object.

            

In medicine, ultrasonic is used as a diagnostic tool, to destroy diseased tissue, 
and to repair damaged tissue. Ultrasound examination of the heart is known as 
echocardiography.

Many animals hear a much wider range of frequencies than human beings do. For 
example, dog whistles vibrate at a higher frequency than the human ear can detect, 
while evidence suggests that dolphins and whales communicate at frequencies 
beyond human hearing (ultrasound) see Fig.1.25 below.(Cutnell & Johnson, 2006). 

         

         b. Wavelength
Wavelength is the distance covered by a wave in a period. It is represented by 
the separation between a point on one wave and a similar point on the next cycle 
of the wave. For a transverse wave, wavelength is measured between adjacent 
crests or between adjacent troughs. For a longitudinal wave such as sound wave, 
wavelength is the distance between adjacent compressions or rarefaction.

      c. Speed of sound
For a periodic wave, the shape of the string at any instant is a repeating pattern. The 
length of one complete wave pattern is the distance from one crest to the next or 
from one trough to the next or from any point to the corresponding point on the next 
repetition of the wave shape. We call this distance the wavelength of the wave, 
denoted by the Greek letter lambda (λ). 

The wave pattern travels with constant speed and advances a distance of one 

wavelength in a time interval of one period T. So, the wave speed is given by 

                              

where f is the frequency of the wave.

Sound travels faster in liquids and solids than in gases, since the particles in liquids 
and solids are closer together and can respond more quickly to the motion of 
their neighbors. As examples, the speed of sound is 331 m/s in air, 1500 m/s in 
water and 5000 m/s in iron (though these mediums the seed of sound can change 

depending on temperature and pressure). Sound does not travel in vacuum.

         

         

          

       

        

            d. Amplitude

The amplitude of a wave is the maximum displacement of the medium from its rest 
position. The amplitude of a transverse wave is the distance from the rest position 

to a crest or a trough. The more energy a wave has, the greater is its amplitude.

Application activity 1.2

1. The correct statement about sound waves is that: 
      A. They are transverse waves
      B. They can be polarized
     C. They require material medium to propagate
2. Sound travels in 
     A. Air C. Water
     B. Iron D. All of these
3. Two men talk on the moon. Assuming that the thin layer of gases on the 
     moon is negligible, which of the following is the right answer:
    A. They hear each other with lower frequency 
    B. They hear each other with higher frequency
    C. They can hear each other at such frequency 
    D. They cannot hear each other at all
4. Do you expect an echo to return to you more quickly on a hot day or a 
    cold day? Explain your answer.
   A. Hot day.
   B. Cold day.
   C. Same on both days.
5. A sound wave is different than a light wave in that a sound wave is:
    A. Produced by an oscillating object and a light wave is not.
    B. Not capable of traveling through a vacuum.
    C. Not capable of diffracting and a light wave is.
    D. Capable of existing with a variety of frequencies and a light wave 
        has a single frequency.
6. A spider of mass 0.30 g waits in its web of negligible mass see Fig. 
   below. A slight movement causes the web to vibrate with a frequency 

   of about 15 Hz.

              

a. Estimate the value of the spring stiffness constant k for the web assuming 
    simple harmonic motion. 
b. At what frequency would you expect the web to vibrate if an insect of 
   mass 0.10 g were trapped in addition to the spider?
7. Dolphins use sound waves to locate food. Experiments have shown 
that a dolphin can detect a 7.5 cm target 110 m away, even in murky 
water. For a bit of “dinner” at that distance, how much time passes 
between the moment the dolphin emits a sound pulse and the moment 
the dolphin hears its reflection and thereby detects the distant target?

8. By what factor would you have to multiply the tension in a stretched 
string in order to double the wave speed? Explain your answer.

9. (a) The range of audible frequencies is from about 20 Hz to 20 000 Hz.
            What is the range of the wavelengths of audible sound in air? 
    (b) The range of visible light extends from 400 nm to 700 nm. What is 
           the range of visible frequencies of light? 
   (c) Surgeons can remove brain tumors by using a cavitron ultrasonic 
         surgical aspirator, which produces sound waves of frequency 23 
       kHz. What is the wavelength of these waves in air? 
  (d) Sound having frequencies above the range of human hearing (about 
        20 000 Hz) is called ultrasound. Waves above this frequency can 
       be used to penetrate the body and to produce images by reflecting 
       from surfaces. In a typical ultrasound scan, the waves travel through 
       body tissue with a speed of 1500 m/s. For a good, detailed image, 
      the wavelength should be no more than 1.0 mm. What frequency 

      sound is required for a good scan?

        1.3 CHARACTERISTICS OF MUSICAL NOTES

           Activity 1.3
The physical characteristics of a sound wave are directly related to the 
perception of that sound by a listener. 
1. What is the difference between the sound of whistle and that of drum?
2. Mutoni is playing the same notes on different musical instruments, can 
     you predict which musical instruments is played without seeing them? 

    Explain your answers.

A musical note is produced by vibrations that are regular and repeating, i.e. by 
periodic motion. Non-periodic motion results in noise which is not pleasant to the 
ear. Many behaviors of musical note can be explained using a few characteristics: 
intensity and loudness, frequency and pitch, and quality or timber

1.3.1. Pitch and frequency
The sound of a whistle is different from the sound of a drum. The whistle makes a 
high sound. The drum makes a low sound. The highness or lowness of a sound is 
called its pitch. The higher the frequency, the higher is the pitch. The frequency of 
an audible sound wave determines how high or low we perceive the sound to be, 
which is known as pitch.

Frequency refers to how often something happens or in our case, the number of 
periodic, compression-rarefaction cycles that occur each second as a sound wave 
moves through a medium and is measured in Hertz (Hz) or cycles/second. The term 
pitch is used to describe our perception of frequencies within the range of human 
hearing.

If a note of frequency 300 Hz and note of 600 Hz, are sounded by a siren, the 
pitch of the higher note is recognized to be an upper octave of the lower note. 
The musical interval between two notes is an upper octave if the ratio of their 
frequencies is 2:1. It can be shown that the musical interval between two notes 
depends on the ratio of their frequencies, and not on the actual frequencies.

Whether a sound is high-pitched or low-pitched depends on how fast something 
vibrates. Fast vibrations make high-pitched sounds. Slow vibrations make low 
pitched sounds. 

Do not confuse the term pitch with frequency. Frequency is the physical 
measurement of the number of oscillations per second. Pitch is a psychological 
reaction to sound that enables a person to place the sound on a scale from high 
to low, or from treble to bass. Thus, frequency is the stimulus and pitch is the response.
 Although pitch is related mostly to frequency, they are not the same. A 
phrase such as “the pitch of the sound” is incorrect because pitch is not a physical 

property of the sound. The octave is a measure of musical frequency.

1.3.2 Intensity, amplitude and ear response

A police siren makes a loud sound. Whispering makes a soft sound. Whether a 
sound is loud or soft depends on the force or power of the sound wave. Powerful 
sound waves travel farther than weak sound waves. To talk to a friend across the 
street you have to shout and send out powerful sound waves. Your friend would 
never hear you if you whispered.

A unit called the decibel measures the power of sound waves. The sound waves 
of a whisper are about 10 decibels. Loud music can have a level of 120 decibels 
or more. Sounds above 140 decibels can actually make your ears hurt. The energy 
carried by a sound wave is proportional to the square of its amplitude. The energy 
passing in a unit area per unit time is called the intensity of the wave.

     
        
Sound intensity level
To the human ear the change in loudness when the power of a sound increases 
from 0.1 W to 1.0 W is the same as when 1W to 10 W. The ear responds to the 
ratio of the power and not to their difference.

We measure sound level intensity in terms of “decibels”. The unit bel is named after 

the inventor of the telephone, Alexander Graham Bell (1847–1922). 

The decibel is a “relative unit” which is actually dimensionless, comparing a given 

sound to a standard intensity which represents the smallest audible sound:

        

The intensity of 0dB represents the softest audible sound (threshold of human 
hearing), while 80 dB (i.e., moderately loud music) represents an intensity which is 

one hundred million times greater. 

      

The physical characteristics of a sound wave are directly related to the perception 
of that sound by a listener. For a given frequency the greater the pressure amplitude 
of a sinusoidal sound wave, the greater the perceived loudness. 

The loudness or softness of sound depends on the intensity of the sound wave 
reaching the person concerned. Loudness is a subjective quantity unlike intensity.
Sound that is not wanted or unpleasant to the ear is called noise. High intensity 
can damage hearing. The higher the intensity, the louder is the sound. Our ears, 
however, do not respond linearly to the intensity. A wave that carries twice the 

energy does not sound twice as loud. 

Anatomy of human ear
The human ear is a remarkably sensitive detector of sound. Mechanical detectors 
of sound can barely match the ear in detecting low intensity sounds. The ear has a 
function of transforming the vibrational energy of waves into electrical signals that 
are carried to the brain by ways of nerves as does a microphone. 

The ear consists of three main parts: the outer ear, the middle ear and the inner ear.

In the outer ear, sounds waves from the outside travel down the ear canal to the 
eardrum which vibrates in response to the colliding waves.The inner ear consists 
of three small bones known as the hammer, anvil and stirrup which transfer the 
vibrations of the eardrum to the inner ear at the oval window.

The function of the inner ear is to transduce vibration into nervous impulses. While 
doing so, it also produces a frequency (or pitch) and intensity (or loudness) analysis 
of the sound. Nerve fibres can fire at a rate of just under 200 times per second. 
Sound level information is conveyed to the brain by the rate of nerve firing, for 
example, by a group of nerves each firing at a rate at less than 200 pulses per 
second. They can also fire in locked phase with acoustic signals up to about 5 
kHz. At frequencies below 5 kHz, groups of nerve fibres firing in lock phase with 
an acoustic signal convey information about frequency to the brain. Above about 
5 kHz frequency information conveyed to the brain is based upon the 
place of stimulation on the basilar membrane. As an aside, music translated 
up into the frequency range above 5 kHz does not sound musical. (Hallowell, Davis; 

Richard,S., 1970)

This delicate system of levers, coupled with the relatively large area of the eardrum 
compared to the area of the oval window, results in pressure being amplified by 
a factor of about 40. The inner ear consists of the semicircular canals, which are 
important for controlling balance, and the liquid filled cochlea where the vibrational 

energy of sound waves is transformed into electrical energy and sent to the brain.

Logarithmic response of the ear versus intensity
The ear is not equally sensitive to all frequencies. To hear the same loudness for 
sounds of different frequencies requires different intensities. Studies done over 

large numbers of people have produced the curves shown on Fig.1.28. 

   

On this graph, each curve represents sounds that seemed to be equally loud. The 
number labelling each curve represents the loudness level which is numerically 
equal to the sound level in dB at 1000 Hz. The units are called phons.

Example: The curve labelled 40 represents sounds that are heard by an average 
person to have the same loudness as 1000 Hz sound with a sound level of 40 dB. 
From this 40 phon curve, we see that a 100 Hz tone must be at a level of about 
62 dB to be perceived as loud as a 1000 Hz tone of only 40 dB.

Two aspects of any sound are immediately evident to human listener: loudness 
and the pitch. Each refers to a sensation in the consciousness of the listener. But 
to each of these subjective sensations there corresponds a physically measurable 
quantity.

Loudness refers to the intensity in the sound wave. Intensity is related to the 
energy transported by a wave per unit time across a unit area perpendicular to the 
energy flow. Intensity is proportional to the square of the wave amplitude. 

A unit called a phon is used to express loudness numerically. Phons differ from 
decibels because the phon is a unit of loudness perception, whereas the decibel is 
a unit of physical intensity. Fig.1.28 shows the relationship of loudness to intensity 
(or intensity level) and frequency for persons with normal hearing. The curved lines 
are equal-loudness curves. Each curve is labelled with its loudness in phons. Any 
sound along a given curve is perceived as equally loud by the average person. The 
curves were determined by having large numbers of people compare the loudness 
of sounds at different frequencies and sound intensity levels. At a frequency of 
1000 Hz, phons are taken to be numerically equal to decibels.

Because of this relationship between the subjective sensation of loudness and the 
physically measurable quantity intensity, sound intensity levels are usually specified 
on a logarithmic scale. The unit of this scale is a bel, after the inventor Alexander 
Graham Bell. 

    1.3.3 Quality or timbre
If the same note is sounded on the violin and then on the piano, an untrained listener 
can tell which instrument is being used, without seeing it. We would never mistake 
a piano for flute. We say that the quality or timbre of note is different in each case. 
The manner in which an instrument is played strongly influences the sound quality.

Two tones produced by different instruments might have the same fundamental 
frequency (and thus the same pitch) but sound different because of different 
harmonic content. The difference in sound is called tone color, quality, or timbre.

A violin has a different timbre than a piano.

             Application activity 1.3

1. Complete each of the following sentences by choosing the correct 
      term from the following words: loudness, pitch, sound quality, echoes, 
      intensity and noise
a. The ------------ of a sound wave depends on its amplitude
b. Reflected sound waves are called ---------------------------
c. Two different instruments playing the same note sound different because 
      of ------------------
2. Plane sound wave of frequency 100 Hz fall normally on a smooth wall. 
     At what distances from the wall will the air particles have:
a. Maximum amplitude of vibration
b. Minimum amplitude of vibration? 
     Give reasons for your answer. The speed of sound in air may be taken 
      as 340 m/s
3. A boy whistles a sound with the power of 4 0.5 10 W− × . What will be his 
sound intensity at a distance of 5 m?
4. Calculate the intensity level equivalent to an intensity 1nW/m2
5. If the statement is true, write true. If it is false, change the underlined 
word or words to make the statement true.
a. Intensity is mass per unit volume.
b. Loudness is how the ear perceives frequency
c. Music is a set of notes that are pleasing
6. The sound level of sound whose intensity is 10 2 I Wm 1.0 10 / − = × what 

     will be the sound intensity level?

1.4 THE DOPPLER EFFECT AND ITS APPLICATIONS

              Activity 1.4

1. People use sound for other things other than talking and making music. 
    In your own words, give more examples and explanations to support this 
    statement.
2. Imagine you are standing beside a road and a police car with its siren 
   turned on, drives by you. What do you notice about the heard sound? 
3. In the second case, the same police car turned and comes towards you. 
    Comment on the heard sound 

4. Compare and contrast the sounds heard in case 2 and 3.

       1.4.1 Doppler Effect

Doppler’s effect is the apparent variation in frequency of a wave due to the relative 
motion of the source of the wave and the observer.

The effect takes its name from the Austrian Mathematician Christian Johann Doppler 
(1803-1853), who first stated the physical principle in 1842. Doppler’s principle 
explains why, if a source of sound of a constant pitch is moving toward an observer, 
the sound seems higher in pitch, whereas if the source is moving away it seems 
lower. This change in pitch can be heard by an observer listening to the whistle of 

an express train from a station platform or another train. 

                   

          

Hence the frequency you hear is higher than the frequency emitted by the 
approaching source. 

       Example 1.10

If a source emits a sound of frequency 400 Hz when is at rest, then when the 
source moves toward a fixed observer with a speed of 30 m/s, what frequency 
does the observer hears knowing that the speed of a sound in air at room 

temperature is 343m/s?

 

               

          

The upper signs apply if source and/or observer move toward each other. The 
lower signs apply if they are moving apart. The word toward is associated with 
an increase in observed frequency. The words away from are associated with a 
decrease in observed frequency.

Although the Doppler’s effect is most typically experienced with sound waves, it 
is a phenomenon that is common to all waves. For example, the relative motion 
of source and observer produces a frequency shift in light waves. The Doppler’s 
effect is used in police radar systems to measure the speeds of motor vehicles. 
Likewise, astronomers use the effect to determine the speeds of stars, galaxies, 

and other celestial objects relative to the Earth.

Example1.13

As an ambulance travels east down a highway at a speed of 33.5 m/s, its siren 
emits sound at a frequency of 400 Hz. What frequency is heard by a person in a 
car traveling west at 24.6 m/s
a. as the car approaches the ambulance and 
b. as the car moves away from the ambulance?
c. Suppose the car is parked on the side of the highway as the ambulance 
    speeds by. What frequency does the person in the car hear as the 

    ambulance (i) approaches and (ii) recedes?

           

     1.4.2 Uses of Doppler Effect

       Astronomy

Doppler Effect is used to measure the speed at which stars and galaxies are 
approaching or receding from us, in a mechanism named red shift or blue shift. 
Redshift happens when light seen coming from an object that is moving away is 
proportionally increased in wavelength, or shifted to the red end of the spectrum. 
Vice versa occurs with blue shift. Since blue light has a higher frequency than red 
light, the spectral lines of an approaching astronomical light source exhibit a blue 
shift and those of a receding astronomical light source exhibits a redshift. 

       Medical imaging
In medicine, the Doppler Effect can be used to measure the direction and speed 
of blood flow in arteries and veins. This is used in echocardiograms and medical 
ultrasonography and is an effective tool in diagnosis of vascular problems. 

       Radar
The Doppler Effect is used to measure the velocity detected objects where a radar 
beam is fired at a moving target. For example, the police use radar to detect a 
speeding vehicle. Radio waves are fired using a radar gun at the moving vehicle. 
The velocity is calculated using the difference between the emitted frequency and 
the reflected frequency. In a similar way, Doppler radar is used by weather stations 

to calculate factors like wind speed and intensity

     Application activity 1.4

1. Choose the best answer: Bats can fly in the dark without hitting 
     anything because
A. They are flying mammals           C. They are guided by ultrasonic waves 
      produced by them
B. Their night vision is going           D. Of no scientific reason
 2. Discuss application of sound waves in medicine and navigation
3. Explain how sonar is used to measure the depth of a sea
4. a. What is meant by Doppler Effect?
b. A police car sound a siren of 1000 Hz as it approaches a stationary 
     observer at a speed of 33.5 m/s. What is the apparent frequency of 
    the siren as heard by the observer if the speed of sound in air is 340 
    m/s.

c. Discuss applications of the Doppler Effect.

                                          Skills Lab 1

In this activity, you will design any musical instrument of your choice.
Procedures:
• Think of the instrument you wish to design. You may have two alternatives.
• Check whether the materials can be locally available in your area
• When you have all the required materials, start making it. You can find a 
   model instrument for reference.
• After you have designed your instrument, try to experiment (play it) to 
   check whether it is functioning. In case it is not functioning, try to design 
   it until it works
• When you are done, try to present it to the whole class in presence of 
   your tutor.
Note: You can ask a place at your school where you can keep your instrument 

for future use by either other students or tutors.

             End of unit 1 assessment  

  For question 1 to 6, choose the letter of the best answer
1. Which of the following affects the frequency of wave?
A. Reflection C. Diffraction
B. Doppler Effect D. All of the above
2. Consider the following statements:
I) Recording of sound on tapes was first invented by Valdemar Poulsen.
II) Audio tapes have magnetic property.
III) The tapes may also be made of PVC (Polyvinyl-chloride)
2. Considering the above statements in question 2 choose the letter of the 
best answer:
A. I, II, and III all are correct.                              C. I and II are correct, III is 
wrong
B. I, II, and III all are wrong                                D. I and II are wrong, III is 
correct
3. Nodes are
A. Positions of maximum displacement
B. Positions of no displacement
C. A position between no displacement and maximum displacement
D. None of these
4. Sound waves are:
A. Transverse waves characterized by the displacement of air molecules.
B. Longitudinal waves characterized by the displacement of air molecules.
C. Longitudinal waves characterized by pressure differences.
D. Both (B) and (C).
E. (A), (B), and (C).
5. In which of the following is the wavelength of the lowest vibration mode 
    the same as the length of the string or tube?
A. A string.                                                                                    D. An open tube.
B. A tube closed at one end.                                                 E. None of the above.
C. All of the above.
6. When a sound wave passes from air into water, what properties of the 
    wave will change?
A. Frequency. D. Wavelength.
B. Wave speed. E. Both frequency and wavelength.
C. Both wave speed and wavelength.
7. Does the phenomenon of wave interference apply only to sinusoidal 
    waves? Explain.
8. As oppositely moving pulses of the same shape (one upward, one 
   downward) on a string pass through each other, there is one instant at 
   which the string shows no displacement from the equilibrium position 
   at any point. Has the energy carried by the pulses disappeared at this 
    instant of time? If not, where is it?
9. Can two pulses traveling in opposite directions on the same string 
    reflect from each other? Explain. 
10. When two waves interfere, can the amplitude of the resultant wave 
      be greater than the amplitude of any of the two original waves? Under 
      which conditions?
11. When two waves interfere constructively or destructively, is there any 
     gain or loss in energy? Explain.
12. Explain why your voice seems to sound better than usual when you 
      sing in the shower.
13. An airplane mechanic notices that the sound from a twin-engine aircraft 
       rapidly varies in loudness when both engines are running. What could 
      be causing this variation from loud to soft?
14. Explain how a musical instrument such as a piano may be tuned by 
       using the phenomenon of beats.
15. Fill in the gap
A. As a sound wave or water ripple travels out from its source, its ---------
----- decreases. 
B. The vibrating air in a/an ----------------------------- has displacement 
      antinodes at both ends.
C. For a /an ……………., the fundamental corresponds to a wavelength 
    four times the length of the tube.
D. The ……………….. refers to the change in pitch of a sound due to the 
     motion either of the source or of the observer. If source and observerare 
    approaching each other, the perceived pitch is …….. If they are moving 
    apart, the perceived pitch is …………….
16. A bat, moving at 5.00 m/s, is chasing a flying insect. If the bat emits a 
      40.0 kHz chirp and receives back an echo at 40.4 kHz, at what speed 
     is the insect moving toward or away from the bat? (Take the speed of 
    sound in air to be v = 340 m/s.)
17. If you hear the horn of the car whose frequency is 216 Hz at a frequency 
     of 225 Hz, what is their velocity? Is it away from you or toward you? The 
     speed of sound is 343 m/s
18. You run at 12.5 m/s toward a stationary speaker that is emitting a 
      frequency of 518 Hz. What frequency do you hear? The speed of 
      sound is 343 m/s
19. If you are moving and you hear the frequency of the speaker at 557 
     Hz, what is your velocity? Is it away from or toward the speaker? The 

     speed of sound is 343 m/s

 20. Read the following text and answer the question
Researchers have known for decades that whales sing complicated songs. 
Their songs can last for 30 min and a whale may repeat the song for two or 
more hours. Songs can be heard at a distances of hundreds of kilometers. 
There is evidence that whales use variations in the songs to tell other whales 
about the location of food and predators. Only the male whales sing, which 
has led some researchers to think that songs are also used to attract a male.

The whale songs may be threatened by noise pollution. In the past 50 years, 
ocean noise has increased due to human activities. Goods are transported 
across the ocean in larger ships than ever before. Large ships use bigger 
engines. They produce low-frequency noise by stirring up air bubbles with their 
propellers. Unfortunately, whales also use low-frequency sound in their songs, 
perhaps because these sounds carry further than high-frequency sounds in 
the ocean. Propeller noise from large ships is loud enough to interfere with 
whale songs at a distance of 20 km.

Question: Are regulations needed to protect whales from noise?
In your own words, describe the major issue that needs to be resolved about 
ocean noise pollution. List three arguments for those who think regulations 
should require large ships to reduce noise pollution. List three arguments for 

those who think regulations are not necessary.