• ### Unit1: SOUND WAVES

Fig.1. 1: People listening to music

Key unit Competence

By the end of the unit I should be able to analyze the effects of sound waves in elastic medium

My goals

• Describe how sound propagates through a substance

• Give the characteristics of sound.

• Relate loudness and pitch to amplitude and frequency

• Carry out calculations relating decibels and intensity

• Establish relationship between characteristics of notes and sound waves

• Explain beats and establish beat frequency

• Explain Doppler – Fizeau effect.

• Give examples of musical pipe instruments.

• Establish the fundamental frequency and 2nd harmonic, 3rd harmonic, in vibrating strings and in pipes

• Explain Doppler – Fizeau effect. • Give examples of musical pipe instruments.

• Establish the fundamental frequency and 2nd harmonic, 3rd harmonic, in vibrating strings and in pipes

Introductory activity

What properties explain most the behavior  of sound?

1. Most people like to listen to music, but hardly anyone likes to listen to noise. What is the difference between a musical sound and noise?

2. A guitarist plays any note. The sound is made by the vibration of the guitar string and propagates as a wave through the air and reaches your ear. Which of the following statement is the right?

• The vibration on the string and the vibration in the air have the same wavelength.

• They have the same frequency.

• They have the same speed.

• None of the above is the same in the air as it is on the string.

1.1 CHARACTERISTICS AND PROPERTIES OF SOUND WAVES

Activity 1.1: Properties of sound

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 behaves 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 teacher and doubles as a Physics laboratory attendant.

1.1.1 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. Absorption is the phenomenon of the wave where the energy of sound wave gets transformed from one form to another. The high frequency sound waves are more easily absorbed than low frequency sounds. It happens most with the soft materials.

1.1.2 Characteristics of sound waves

Activity 1.2: Characteristics of sound waves

1. How to calculate the speed of sound waves in different materials.

2. How to calculate the intensity of a sound wave.

3. From the Fig.1.2, can you hear the ultrasound waves that a bat uses for echolocation? Why or why not?

Fig.1. 2: Range of frequencies heard by various animals and human (Randall & Knight.,Physics for scientists and engineers: Stategic approach., 2008)

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 soundlies 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.

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 with each other, even when they are separated by many kilometers. Rhinoceros also use infrasonic as low as 5 Hz to call one another.

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. 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) (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

(1.01)

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

Example 1.1 Wavelength of a musical sound

1. Sound waves can propagate in air. The speed of the sound depends on temperature of the air; at 200  C it is 344 m/s it is. What is the wavelength of a sound wave in air if the frequency is 262 Hz  (the approximate frequency of middle C on a piano)?

Using Equation of wave (1.01):  λ=V/f = (344m/s)/262Hz=1.31m

Factors which affect the velocity of sound in air

• The speed of sound waves in a medium depends on the compressibility and density of the medium. If the medium is a liquid or a gas and has a bulk modulus Band density ρ , the speed of sound waves in that medium is given by:

(1.02)

It is interesting to compare this expression with the equation  applicable to transverse waves on a string. In both cases, the wave speed depends on an elastic property of the medium (bulk modulus B or tension in the string T) and on an inertial property of the medium (the density ρ or linear mass µ ).     In fact, the speed of all mechanical waves follows an expression of the general form (1.03)

For longitudinal sound waves in a solid rod of material, for example, the speed of sound depends on Young’s modulus Y and the density ρ • Changes of pressure have no effect on the velocity of sound in air. Sir Isaac Newton showed that:

(1.04)

In accordance with Boyle’s law, if the pressure of a fixed mass of air is doubled, the volume will be halved. Hence the density will be doubled. Thus at constant temperature, the ratio P/ρ will always remain constant no matter how the pressure may change. The speed of sound increases with temperature If the air temperature increases at constant pressure the air will expand according to Charles’ law, and therefore become less dense.

The ratio P/ρ will therefore increase, and hence the speed of sound increases with temperature.

For sound traveling through air, the relationship between wave speed and medium temperature is  (1.05)

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.

1.1.3 Checking my progress

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

b. Water

c. 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?

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.

Fig.1. 3 A spider of mass waits in its web

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?

1.2 PRODUCTION OF STATIONARY SOUND WAVES

Fig.1. 4: A guitarist.

Activity 1.3: Production of stationary sound waves.

Look at the Fig.1.4 of guitarist and then answer the following question.

1. How do vibrations cause sound?

2. What determines the particular frequencies of sound produced by an organ or a flute?

3. How resonance occurs in musical instruments?

4. How to describe what happens when two sound waves of slightly different frequencies are combined?

1.2.1 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. 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

Quick check 1.1: Standing sound waves are produced in a pipe that is 1.20 m long. For the fundamental and first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes and the pressure nodes if the pipe is open at both ends.

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

The longest 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.

Another way to analyze the vibrations in a uniform tube is to consider a description in terms of the pressure in the air. Where the air in a wave is compressed, the pressure is higher, whereas in a wave expansion (or rarefaction), the pressure is less than normal.We call a region of increased density a compression; a region of reduced density is a rarefaction.

The wavelength is the distance from one compression to the next or from one rarefaction to the next.

Quick check 1.2: Standing sound waves are produced in a pipe that is 1.20 m long. For the fundamental and first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes and the pressure nodes if the pipe is closed at the left end and open at the right end.

1.2.2 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.1.12. 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.

The normal modes of vibration form a harmonic series: (b) the fundamental note (first harmonic); (c) First overtone (second harmonic); (d) the second overtone (third harmonic) (Halliday, Resneck, & Walker, 2007).

1.2.3. Wave Interference and Superposition

a. Wave interference

Up to this point we’ve been discussing waves that propagate continuously in the same direction. But when a wave strikes the boundaries of its medium, all or part of the wave is reflected

When you yell at a building wall or a cliff face some distance away, the sound wave is reflected from the rigid surface and you hear an echo. When you flip the end of a rope whose far end is tied to a rigid support, a pulse travels the length of the rope and is reflected back to you. In both cases, the initial and reflected waves overlap in the same region of the medium. This overlapping of waves is called interference

In general, the term “interference” refers to what happens when two or more waves pass through the same region at the same time Fig.1.14 shows an example of another type of interference that involves waves that spread out in space.

Two speakers, driven in phase by the same amplifier, emit identical sinusoidal sound waves with the same constant frequency. We place a microphone at point P in the figure, equidistant from the speakers. Wave crests emitted from the two speakers at the same time travel equal distances and arrive at point P at the same time; hence the waves arrive in phase, and there is constructive interference.

The total wave amplitude at P is twice the amplitude from each individual wave, and we can measure this combined amplitude with the microphone.

Now let’s move the microphone to point Q, where the distances from the two speakers to the microphone differ by a half-wavelength. Then the two waves arrive a half-cycle out of step, or out of phase; a positive crest from one speaker arrives at the same time as a negative crest from the other. Destructive interference takes place, and the amplitude measured by the microphone is much smaller than when only one speaker is present. If the amplitudes from the two speakers are equal, the two waves cancel each other out completely at point Q, and the total amplitude there is zero.

Activity 1.4:

Problem 1

The Adventures of Marvin the Mouse: You and your friend are walking down by the pool when you hear a cry for help. Poor Marvin the Mouse has fallen into the pool and needs your help. The sides of the pool are to slippery for Marvin to climb out but there is an inner tube anchored in the center of the pool. Oh no! The sides of the inner tube are too slippery and high for Marvin to climb. He’s getting tired and can’t swim to the sides; he has just enough energy to float by the inner tube. Having studied about waves, you and your friend take up positions on opposite sides of the pool. How did you help Marvin get safely onto the inner tube?

Problem 2: Dance club designer

You are the designer of a new Dance Club. You have been informed that you need to design the club in such a way that the telephone is placed in a location that allows the customers to hear the people on the other side. The phone company states that they can only put the phone line in at a point 20 m from the stage. Develop a model which allows the customers to use the phone with the least amount of trouble given that the phone must be placed at a distance of 20 m, (2/3 the room size), from the stage. This will be an area where there will be virtually no sound.

c. 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 exhibits large amplitude when driven at any of its natural frequencies, these frequencies are often referred to as resonance frequencies. Fig.1.15 shows the response of an oscillating system to various driving frequencies, where one of the resonance frequencies of the system is denoted by fo.

One of our best models of resonance in a musical instrument is a resonance tube. This is a hollow cylindrical tube partially filled with water and forced into vibration by a tuning fork (Fig.1.16). The tuning fork is the object that forced the air, inside the resonance tube, into resonance.

As the tines of the tuning fork vibrate at their own natural frequency, they created sound waves that impinge upon the opening of the resonance tube. These impinging sound waves produced by the tuning fork force air inside of the resonance tube to vibrate at the same frequency. Yet, in the absence of resonance, the sound of these vibrations is not loud enough to discern.

Resonance only occurs when the first object is vibrating at the natural frequency of the second object. So if the frequency at which the tuning fork vibrates is not identical to one of the natural frequencies of the air column inside the resonance tube, resonance will not occur and the two objects will not sound out together with a loud sound. But the location of the water level can be altered by raising and lowering a reservoir of water, thus decreasing or increasing the length of the air column.

So by raising and lowering the water level, the natural frequency of the air in the tube could be matched to the frequency at which the tuning fork vibrates. When the match is achieved, the tuning fork forces the air column inside of the resonance tube to vibrate at its own natural frequency and resonance is achieved. The result of resonance is always a big vibration - that is, a loud sound. 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. 1.18)

d. 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 equal amplitudes and slightly different frequencies as shown on the figure below.

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. 1.19; the red line represents the 50 Hz wave, and the blue line represents the 60 Hz wave. The lower graph in Fig. 1.18 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.. Consider two sound waves of equal amplitude traveling through a medium with slightly different frequencies f1 and f2atchosen point x = 0:

Quick check 1.4: A tuning fork produces a steady 400 Hz tone. When this tuning fork is struck and held near a vibrating guitar string, twenty beats are counted in five seconds. What are the possible frequencies produced by the guitar string?

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

1.3 CHARACTERISTICS OF MUSICAL NOTES

Activity 1.5: Characteristics of musical notes

The physical characteristics of a sound wave are directly related to the perception of that sound by a listener. Before you read this section answer these questions. As you read this section answer again these questions. Compare your answer.

1. What is the difference between the sound of whistle and that of drum?

2. Can you tell which musical instrument is played if the same note is played on different instrument without seeing it? Explain

3. How can you calculate the intensity of a sound wave?

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 and amplitude

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 a unit area per unit time is called the intensity of the wave.

The intensity of spherical sound wave at a place p is defined as the energy per second per m2, or power per m2 flowing normally through an area at X. i.e

where r is the distance from the source for a spherical wave

Quick check 1.4: A point source emits sound waves with an average power output of 80.0 W.

a. Find the intensity 3.00 m from the source.

b. Find the distance at which the sound level is 40 dB.

Activity 1.6: Noise or music

Most people like to listen to music, but hardly anyone likes to listen to noise.

1. What is the physical difference between musical sound and noise?

2. What is the effect of noise to human being?

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.

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.

1.3.4 Checking my progress

1. Complete each of the following sentences by choosing the correct term from the word bank: 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 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 0.5x10-4w . What will be his sound intensity at a distance of 5m?

4. Calculate the intensity level equivalent to an intensity 1 nW/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

1.4 APPLICATIONS OF SOUND WAVES

Activity1.7: Doppler Effect and uses of sound waves

1. Why does the pitch of a siren change as it moves past you?

2. How is Doppler’s effect used in communication with satellites?

3. Explain how is the Doppler’s effect used in Astronomy?

4. People use sound for other things other than talking and making music. In your own word, give more examples and explanations to support this statement.

1.4.1 The 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.

Fig.1. 19 C.J.Doppler (Douglass, PHYSICS, Principles with applications., 2014)

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.

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.

Quick check 1.5: Middle C on the musical scale has a frequency of 264 Hz.  What is the wavelength of the sound wave?

1.4.2 Uses of Ultrasonic

a. Echolocation

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 (Cutnell & Johnson, 2006).

The Ultrasonic waves emitted by a dolphin enable it to see through bodies of other animals and people (Fig.1.20). 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.

Fig.1. 21:  The Ultrasonic waves emitted by a dolphin enable it to see through bodies of other animals and people.

Bats also use echo to navigate through air.Bats use ultrasonic with frequencies up to 100 kHz to move around and hunt (Fig.1.23).

Fig.1. 22 Bats use ultrasonic with frequencies up to 100 kHz to move around and hunt

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. Dogs, cats and mice can hear ultrasound frequencies up to 450 kHz. Some animals not only hear ultrasound but also use ultrasonic to see in dark.

b. In medicine

The sonogram is device used in medicine and exploits the reflected ultrasound to create images. This pulse-echo technique can be used to produce images of objects inside the body and is used by Physicians to observe fetuses. Ultrasound use a high frequency in the range of 1 MHz to 10 MHz that is directed into the body, and its reflections from boundaries or interfaces between organs and other structures and lesions in the body are then detected. (Michael, Loannis, & Martha, 2006) Tumors and other abnormal growths can be distinguished; the action of heart valves and the development of a foetus (Fig.1.24) can be examined; and information about various organs of the body, such as the brain, heart, liver, and kidneys, can be obtained.

Although ultrasound does not replace X-rays, for certain kinds of diagnosis it is more helpful. Some tissues or fluid are not detected in X-ray photographs, but ultrasound waves are reflected from their boundaries. Echoes from ultrasound waves can show what is inside the body. Echo is a reflection of sound off the surface of an object.

Fig.1. 23: Ultrasound image as an example of using high-frequency sound waves to see within the human body (Douglass, PHYSICS, Principles with applications., 2014).

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

c. Sonar

The sonar or pulse-echo technique is used to locate underwater objects and to determine distance. A transmitter sends out a sound pulse through the water, and a detector receives its reflection, or echo, a short time later. This time interval is carefully measured, and from it the distance to the reflecting object can be determined since the speed of sound in water is known. The depth of the sea and the location of sunken ships, submarines, or fish can be determined in this way. Sonar also tells how fast and what direction things are moving. Scientists use sonar to make maps of the bottom of the sea.

An analysis of waves reflected from various structures and boundaries within the Earth reveals characteristic patterns that are also useful in the exploration for oil and minerals.

Radar used at airports to track aircraft involves a similar pulse-echo technique except that it uses electromagnetic (EM) waves, which, like visible light, travel with a speed of 3 ×108 m/s. One reason for using ultrasound waves, other than the fact that they are inaudible, is that for shorter wavelengths there is less diffraction so the beam spreads less and smaller objects can be detected.

1.4.3 Uses of infrasonic

Elephants use infrasonic sounds waves to communicate with one another. Their large ears enable them to detect these low frequency sound waves which have relatively long wavelengths. Elephants can effectively communicate in this way even when they are separated by many kilometers. Some animals, such as this young bateared fox, have ears adapted for the detection of very weak sounds.

Fig.1. 24:  Some animals, such as this young bat-eared fox, have ears adapted for the detection of very weak sounds.

1.4.4  Checking my progress

For question 1 to 2: Choose the letter of the best answer

1. Choose the best answer: Bats can fly in the dark without hitting anything because

a. They are flying mammals

b. Their night vision is going

c. They are guided by ultrasonic waves produced by them

d. Of no scientific reason

2. Bats and dolphins use echolocation to determine distances and find prey.

What characteristic of sound waves is most important for echolocation?

a. Sound waves reflect when they hit a surface

b. Sound waves spread out from a source

c. Sound waves diffract around corner

d. Sound waves interfere when they overlap

3. Discuss application of sound waves in medicine and navigation

4. Explain how sonar is used to measure the depth of a sea

5. 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.  Give one application of the Doppler Effect.

1.5 END UNIT ASSESSMENT

1.5.1 Multiple choices question

For question 1 to 6, choose the letter of the best answer

1. Which of the following affects the frequency of wave?

a. Reflection

b. Doppler effect

c. Diffraction 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)Of these statements:

a. I, II, and III all are correct.

b. I, II, and III all are wrong

c. I and II are correct, III  is 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.

b. A tube closed at one end.

c. All of the above.

d. An open tube.

e. E. None of the above.

6. When a sound wave passes from air into water, what properties of the wave will change?

a. Frequency.

b. Wave speed.

c. Both frequency and wavelength.

d. Wavelength.

e. Both wave speed and wavelength.

1.5.2 Structured questions

1. Does the phenomenon of wave interference apply only to sinusoidal waves? Explain.

2. 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?

3. Can two pulses traveling in opposite directions on the same string reflect from each other? Explain.

4. 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?

5. When two waves interfere constructively or destructively, is there any gain or loss in energy? Explain.

6. Explain why your voice seems to sound better than usual when you sing in the shower.

7. 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?

8. Explain how a musical instrument such as a piano may be tuned by using the phenomenon of beats.

9. 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 observer are approaching each other, the perceived pitch is …….. If they are moving apart, the perceived pitch is ……………. 10. 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.)

11. 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

12.  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

13.  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

1.5.3 Essay type question