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Ms. N. May ABC Math Student Copy

Physics Week 8(Sem. 2) Name____________________________

Chapter Summary

Waves and Sound Cont’d

Nature of Waves

There are two common features to all waves; the first is that they are a traveling disturbance. The second feature about waves is that they carry energy from place to place. The following will considering two basic types of waves, transverse and longitudinal. A transverse wave is one in which the disturbance is perpendicular to the direction of travel of the wave. Radio waves, light waves and microwaves are examples of transverse waves. A longitudinal wave is one in which the disturbance is parallel to the line of travel of the wave, sound waves are an example. In addition, some waves are neither all transverse nor all longitudinal. This is the case with water waves that have a nearly circular path, with both longitudinal and transverse components to it.

Periodic Waves

The two above mentioned types of waves are also called periodic waves, because they consist of repeating patterns produced over and over. A cycle is defined as the portion of a wave from the undisturbed position including one trough and one crest back to the undisturbed position; A wave consists of many cycles. The amplitude (A) of a wave is the maximum displacement of a particle of a medium from the particle’s undisturbed position, so the distance from its undisturbed location to the top of the crest (or bottom of the trough). The wavelength (λ) is the horizontal length of one cycle of the wave. The wavelength can also be the distance between two successive troughs or the distance between two successive crests. The period (T) of a wave is the time for one complete cycle or the time for the wave to travel one complete wavelength. The period (T) is related to the frequency () as

1

Basically, the frequency is the inverse of the period. The units for frequency is Hertz (Hz) or cycles/sec. So for example, a wave with a period of 0.1 sec has a frequency of 10 cycles/sec or 10 Hz.

Given all of the above terms the speed of a wave can be calculated. Recall the equation for speed,

For waves there are other variables that represent the distance traveled and time it takes for a wave to travel. Therefore the above equation becomes,

Where ν is the speed of a wave with a known wavelength (λ) and period (T).

Speed of a Wave

The property of the material or medium through which a wave travels determines the speed of the wave. In order for one particle of a wave to move the particle before it must be accelerated by a force (Newton’s 2nd law). But the ability of one particle to pull on its neighboring particle depends on the tension. The greater the tension, the greater the force exerted by one particle on the next particle. Also according to Newton’s 2nd law, the inertia or mass of a particle will influence the speed of the wave. For a given force, a smaller mass has a greater acceleration. Therefore with all other factors the same, a wave travels faster on a string whose particles have less mass. The equation for the speed for a small amplitude wave on a string would be

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In the above equation F is the force and m/L is the linear density of a string (or the mass/unit length). This equation is important in the use of instruments.

Nature of Sound

Sound waves are created by a vibrating object and can only be created or transmitted in a medium (g,l, or s). Sound can not exist in a vacuum. To fully understand sound waves one can think of a vibrating speaker. When a diaphragm moves outward, it compresses the air in front of it. This compression increases the air pressure causing a region of high pressure called a condensation. This region travels away from the speaker at the speed of sound. After the condensation the speaker reverses its motion and moves inward. This inward motion produces a region known as a rarefaction, where the air pressure is slightly less than normal. Following immediately behind the condensation the rarefaction also moves at the speed of sound. It is important to note that sound does not involve the individual air molecules traveling or being moved throughout the length of the wave. Rather, each molecule transferring its energy to the neighboring particle, passing along the condensation or rarefaction.

Each cycle of a sound wave includes a condensation and a rarefaction and the frequency is the number of cycles per second that passes a given location. For example, a sound wave of 1,000 Hz has a 1,000 condensations each followed by a rarefaction per second. A sound with a single frequency is called a pure tone. People can hear frequencies between 20 Hz to 20,000 Hz, with the higher frequencies being more difficult to hear with age. Sound can be generated such that its frequency is less than 20 Hz, this sound is called infrasonic. Rhinoceroses use sounds in this range to communicate with each other. On the other hand, bats use ultrasonic sounds, above 20 kHz, for navigating and finding food. Frequency is a measurable property of a wave; however a listener’s interpretation of frequency (by the brain, subjective) is called pitch. A pure tone with a high (large) frequency is called a high pitch sound, such as

that made by a flute. A tuba is an instrument that makes a low pitch or low frequency sound.

Air pressure can be monitored over the length of a tube to demonstrate the pressure amplitude of a sound wave. If air gauges were placed along the length of a tube the variation in air pressure will appear to be sinusoidal, this graph shows the pressure amplitude. This measures the maximum changes in pressure compared to the atmospheric pressure. The pressure variations due to sound waves are very small. For instance, the pressure variation for a typical conversation between two people is about 3 x 10‐2 Pa. This is compared to atmospheric pressure of 1.01 x 105 Pa.

Loudness is an attribute of the wave that primarily depends on the amplitude; the larger the amplitude the louder the noise. Keeping in mind that amplitude is measureable while loudness is a matter of opinion.

Speed of Sound through Gases

Sound travels through solids, liquids and gases at considerably different speeds. The speed of sound in room temperature air is 343 m/s while it is about 4 times faster in water or 17 times faster in steel. This only proves that the speed of sound depends on the properties of medium that it is traveling through. In a gas, it is only when molecules collide that the condensation or rarefaction can be passed along. So the speed of sound in a gas is most closely related to the average molecular speed of the collisions. The average speed is related to the translational rms‐speed given by the equation

3

Therefore, the speed of sound through an ideal gas is represented by the equation

γ

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Where γ=cp/cv is the ratio of the heat capacity at constant pressure (Cp) to the heat capacity at constant volume (Cv).

Speed of Sound through Liquids

In a liquid the speed of sound depends on the density

(ρ) and the adiabatic bulk modulus (Bad) of the liquid:

ρ

The adiabatic bulk modulus will be provided when needed for particular problems.

Speed of Sound through Solids

In a solid the speed of sound depends on the density (ρ) and Young’s modulus (Y) of the solid:

ρ

Young’s modulus will be provided when needed for particular problems.

Sound Intensity

Sound energy carry energy that has the ability to do work. Like forcing an eardrum to vibrate, or breaking a window from intense vibrations. The amount of energy transported per second by a sound wave is called its power. Power is measured in Joules/sec. or Watts (W). When a sound wave leaves a source (like a speaker) it spreads out passing through larger and larger surface areas. Due to this spreading out, sound intensity is defined to determine the power per area. Sound Intensity (I) is defined by the equation

Where I is the sound intensity in W/m2; P is power (W); and A is the surface area perpendicular to the traveling waves (m2).

For a 1,000 Hz tone, the smallest sound intensity that the human ear can detect is about 1 x 10‐12 W/m2, this intensity is called the human threshold of hearing. On

the other hand, continuous exposure to sound intensities greater than 1 W/m2 can be painful and result in partial/permanent hearing loss.

If a source emits sound uniformly in all directions (similar to a spherical shape) the sound intensity can be rearranged to:

4π

In the above equation r is radius from the center of the sound source. It can be observed that the sound intensity (I) varies inversely to the square of the radius from the center of the source. So if the distance from the center doubles the sound intensity is quartered.

Comparing Sound Intensities

The decibel (dB) is a measurement used to compare the

sound intensity of two sounds. The intensity level (β) in decibels is defined as

β 10 log

Where log is base 10; Io is the reference sound intensity, I is the sound intensity of the sound being compared. Io is typically taken to be the threshold of hearing (Io=1.00x10

‐12 W/m2). The intensity level, or decibel, has no unit like the radian. It is important to note that if the intensity level is zero than that means that the sound intensity is at the threshold of hearing, therefore I=Io.

Experiments show that if the intensity level increases by a factor of 10 dB, the new sound seems approximately twice as loud as the original sound. So with two speaker systems, 20 W and 200 W set to maximum volume the 200 W system will only sound twice as loud.

Doppler Effect

The Doppler effect is the change in pitch or frequency of the sound detected by an observer because the sound source and/or the observer have different velocities with respect to the medium of sound propagation (they are moving).

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If the sound source is moving towards the observer the wavelength will seem as if it has decreased. So as the siren let’s out noise it then moves closer making the next condensation closer to the last condensation previously emitted. This decrease in distance between condensations makes the frequency increase thus effectively decreasing the wavelength. Therefore as a siren is approaching an observer it will get more and more high pitched. The effect on the wavelength will be

Where λ is the wavelength, λ’ is the effective wavelength, νs is the velocity of the source, and T is the period. Therefore the frequency of a source moving towards an observer will be

1

1

Where f’ is the perceived frequency of the source, νs is the velocity of the source, ν is the speed of sound, and f is the true frequency.

If the observer is moving and the sound source is stationary the effects are different. During this situation the observer encounters all of the condensations that he would have if he were stationary, plus an additional number. The frequency the observer would hear ’) would be

1

Using the known fact that ν= , and an observer moving toward the source the equation becomes

1

An observer that moves away from the sound source is moving in the same direction as the sound waves and therefore hears fewer condensations per second than a stationary observer. Thus the frequency equation for an observer moving away from the sound source becomes

1

The previous couple of equations demonstrate the difference in sound when the observer is moving and the sound is stationary versus when the sound is moving and the observer is stationary. Recapping, when the sound is moving the wavelength of the sound changes effecting the frequency that the observer hears. On the other hand, when the observer moves the wavelength of the sound does NOT change. Instead, a moving observer intercepts a different number of wave condensations per second than does a stationary observer thus detecting a different frequency

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1. In the diagram below, a train of waves is moving alonga string.

A) 1 m B) 2 m C) 3 m D) 6 m

What is the wavelength?

2. What is the wavelength of the wave shown in todiagram below?

A) 1 m B) 2 m C) 3 m D) 0.5 m

Base your answer to questions 3 and 4 on the diagrambelow, which represents waves A, B, C, and Dtraveling in the same medium.

A) A and B B) A and C

C) B and D D) C and D

3. Which two waves have the same wavelength?

A) A B) B C) C D) D

4. Which wave has the longest period?

5. In the diagram below, the distance between points A and B on a wave is 0.10 meter.

A) an amplitude of 0.10 m

B) an amplitude of 0.20 m

C) a wavelength of 0.10 m

D) a wavelength of 0.20 m

This wave must have

Base your answer to the following question on thediagram below represents a transverse wave.

A) 1 B) 2 C) 3 D) 1.5

6. How many cycles are shown in the diagram?

7. Which distance represents the wavelength of the waveshown below?

A) A B) B C) C D) D

A) cycles/second B) meters/second

C) seconds D) meters/cycle

8. Which is a unit of wavelength?

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Base your answer to questions 9 and 10 on thediagram below which represents a segment of aperiodic wave traveling to the right in a steel spring.

A) torsional B) longitudinal

C) elliptical D) transverse

9. What type of wave is illustrated by the diagram?

A) 1.0 m B) 2.0 m C) 2.5 m D) 0.4 m

10. What is the wavelength of the wave?

A)

B)

C)

D)

11. Which wave diagram has both wavelength ( ) andamplitude (A) labeled correctly?

A) 1 s B) 0.1 s C) 10 s D) 100 s

12. A periodic wave with a frequency of 10 hertz wouldhave a period of

13. The diagram below represents a transverse wave.


C) A and E D) D and E

The distance between which two points identifies theamplitude of the wave?

Base your answer to questions 14 and 15 on on thediagram below which represents four waves travelingto the right in the same transmitting medium.

A) A B) B C) C D) D

14. Which wave has the greatest frequency

A) A B) B C) C D) D

15. Which wave has the greatest amplitude?

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16. What is the amplitude of the wave represented in thediagram?

A) 1 m B) 2 m C) 3 m D) 6 m

17. The diagram below represents a wave traveling in auniform medium. Which characteristic of the wave isconstant?

A) amplitude B) frequency

C) period D) wavelength

18. In the diagram below, which wave has the largestamplitude?

A) A B) B C) C D) D

A) longitudinal B) transverse

C) latitudinal D) tangential

19. In which type of wave is the disturbance of themedium perpendicular to the direction of travel of thewave?

20. The diagram below shows a transverse water wavemoving in the direction shown by velocity vector v.

A) A B) B C) C D) D

At the instant shown, a cork at point P on the water'ssurface is moving toward

21. As shown in the diagram below, a transverse wave ismoving with velocity v along a rope.

A) down, only

B) up, only

C) down, then up, then down

D) up, then down, then up

In which direction will segment X move as the wavepasses through it?

A) transverse B) longitudinal

C) a microwave D) a radio wave

22. An earthquake is traveling from the west to eastthrough rock. If the particle are vibrating in anorth-south direction, the wave must be classified as

A) light B) radar

C) sound D) photons

23. Longitudinal waves are involved in the transmissionof

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24. The diagram below shows a transverse wave movingtoward the left along a rope.

A) bottom of the page B) top of the page

C) left of the page D) right of the page

At the instant shown, point P on the rope is movingtoward the

25. In the diagram below, a wave of 1.00-meter amplitudeis moving from left to right in an elastic cord.

A) 1.00 meter up

B) 1.00 meter down

C) 0.500 meter up or down

D) 0.00 meter

The displacement of point A after the wave has passedpoint B will be

A) B)

C) D)

26. A transverse wave moves to the right (®) through amedium. Which diagram best represents the motion ofthe molecules of the medium due to the wave motion?

A) electromagnetic B) torsional

C) transverse D) longitudinal

27. If the displacement of particles in a medium is parallelto the direction of travel of the wave, the wave isclassified as

28. The diagram below shows a pulse moving to the rightin a rope A is a point on the rope.

A) B)

C) D)

Which arrow best shows the direction of movement ofpoint A at this instant?

29. The diagram below shows a transverse pulse movingto the right in a string.

A) B)

C) D)

Which diagram best represents the motion of point P as the pulse passes point P?

A) in circles

B) in ellipses

C) parallel to the direction of wave travel

D) perpendicular to the direction of wave travel

30. As a longitudinal wave passes through a medium, theparticles of the medium move

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Base your answer to the following question on thediagram of a Slinky spring shown below.


C) B and C D) B and D

31. The points that represent condensations are

A) longitudinal waves B) transverse waves

C) polarized waves D) torsional waves

32. Compression waves in a spring are examples of

A) 1.2 × 10–3 s B) 2.5 × 10–3 s

C) 9.0 × 10–3 s D) 4.0 × 10–3 s

33. What is the period of a wave with a frequency of 250hertz?

A) 2.27 × 10–3 s B) 0.75 s

C) 1.33 s D) 3.31 × 102 s

34. If the frequency of a sound wave is 440. cycles persecond, its period is closest to

A) B)

C) D)

35. Which graph best represents the relationship betweenthe frequency and period of a wave?

36. The graph below represents the displacement of apoint in a medium as a function of time as a wavepasses through the medium.

A) 1/2 Hz B) 2 Hz

C) 1/4 Hz D) 4 Hz

What is the frequency of the wave?

37. Note that the question below has only three choices.

A) decrease B) increase

C) remain the same

If the amplitude of a wave is increased, the frequencyof the wave will

A) seconds it takes to complete one cycle of a wave

B) cycles of a wave completed in one second

C) points that are in phase along one meter of a wave

D) points that are out of phase along one meter of awave

38. The hertz is a unit that describes the number of

A) v = T

B) v = T

C) v = T

D) v = 2 T

39. Which equation correctly relates the speed v, wavelength , and period T of a periodic wave?

A) thermal energy B) mechanical energy

C) radiant energy D) electrical energy

40. Sound is a form of

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41. Waves are traveling with a speed of three meters persecond toward P as shown in the diagram.

A) 1 m B) 6 m C) 3 m D) 9 m

If three crests pass P in one second, the wavelength is

Base your answer to questions 42 and 43 on on thediagram below which shows a parked police car with asiren on top. The siren is producing a sound with afrequency of 680 hertz, which travels first throughpoint A and then through point B, as shown. The speedof the sound is 340 meters per second.

A) decrease B) increase

C) remain the same

42. If the car were to accelerate toward point A, thefrequency of the sound heard by an observer at point A would

A) 0.50 m B) 2.0 m

C) 2.3 × 105 m D) 2.3 × 106 m

43. What is the wavelength of the sound produced by thecar's siren?

A) 2.5 m/s B) 15 m/s

C) 35 m/s D) 250 m/s

44. What is the velocity of a wave having a frequency of25 cycles per second and a wavelength of 10 meters?

A) 0.50 m B) 2.0 m

C) 5.0 m D) 50. m

45. A periodic wave having a frequency of 5.0 hertz and aspeed of 10. meters per second has a wavelength of

A) 1/4 s B) 2 s C) 1/2 s D) 4 s

46. It takes 1 second for a sound wave to travel from asource to observer A. How long does it take the samesound wave to travel in the same medium to observer B, who is located twice as far from the source asobserver A?

A) halved B) doubled

C) unchanged D) quartered

47. If the period of a wave is doubled, its wavelength willbe

Base your answer to questions 48 and 49 on theinformation and diagram below.

A system consists of an oscillator and a speaker thatemits a 1,000.-hertz sound wave. A microphone detectsthe sound wave 1.00 meter from the speaker.

A) wave speed B) frequency

C) wavelength D) amplitude

48. The microphone is moved to a new fixed location 0.50meter in front of the speaker. Compared to the soundwaves detected at the 1.00-meter position, the soundwaves detected at the 0.50-meter position have adifferent

A) lower B) higher

C) the same

49. The microphone is moved at constant speed from the0.50-meter position back to its original position 1.00meter from the speaker. Compared to the 1,000.-hertzfrequency emitted by the speaker, the frequencydetected by the moving microphone is

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50. The diagram below shows radar waves being emitted from a stationary police car and reflected by amoving car back to the police car.

A) constructive interference B) refraction

C) the Doppler effect D) total internal reflection

The difference in apparent frequency between the incident and reflected waves is an example of

A) red B) blue

C) orange D) yellow

51. An astronomical body emitting high-intensity pulsesof green light is moving toward Earth at high velocity.To an observer on Earth, this light may appear

A) resonance B) the Doppler effect

C) diffraction D) refraction

52. A radar gun can determine the speed of a movingautomobile by measuring the difference in frequencybetween emitted and reflected radar waves. Thisprocess illustrates

A) 30.0 Hz B) 9.19 × 102 Hz

C) 1.00 × 103 Hz D) 1.10 × 103 Hz

53. A police car traveling at a speed of 30.0 meters persecond sounds its siren, which has a frequency of 1.00 ×103 hertz. As the police car approaches astationary pedestrian, the pedestrian detects a sirenfrequency of

A) 1,900 Hz B) 2,000 Hz

C) 2,100 Hz D) 4,000 Hz

54. The driver of a car hears the siren of an ambulancewhich is moving away from her. If the actualfrequency of the siren is 2,000 hertz, the frequencyheard by the driver may be

A) moving toward the police officer

B) moving away from the police officer

C) not moving

55. A police officer's stationary radar device indicates thatthe frequency of the radar wave reflected from anautomobile is less than the frequency emitted by theradar device. This indicates that the automobile is

A) decreases in amplitude and decreases in frequency

B) decreases in amplitude and increases in frequency

C) increases in amplitude and decreases in frequency

D) increases in amplitude and increases in frequency

56. A car’s horn produces a sound wave of constantfrequency. As the car speeds up going away from astationary spectator, the sound wave detected by thespectator

A) he moves toward the source at a constant speed

B) the source moves away from him at a constantspeed

C) he accelerates toward the source

D) the source accelerates away from him

57. A source of waves and an observer are movingrelative to each other. The observer will detect asteadily increasing frequency if

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Base your answer to the following question on thediagram below which represents the wave patternproduced by a vibrating source moving linearly in ashallow tank of water. The pattern is viewed fromabove and the lines represent wave crests.

A) lower B) higher

C) the same

58. Compared to the frequency of the waves observed atpoint D, the frequency of the waves observed at point B is

Base your answer to the following question on thediagram below which represents wave fronts around asound source that is moving with a constant velocitythrough air. The source produces sound waves of aconstant frequency

A) interference B) diffraction

C) reflection D) the Doppler effect

59. The diagram illustrates

A) higher frequency and shorter wavelength

B) higher frequency and longer wavelength

C) lower frequency and shorter wavelength

D) lower frequency and longer wavelength

60. A source of sound waves approaches a stationaryobserver through a uniform medium. Compared to thefrequency and wavelength of the emitted sound, theobserver would detect waves with a

61. The vibrating tuning fork shown in the diagram belowproduces a constant frequency. The tuning fork ismoving to the right at a constant speed, and observersare located at points A, B, C, and D. Which observerhears the lowest frequency?

A) A B) B C) C D) D

A) lower B) higher

C) the same

62. The driver of a car blows the horn as the carapproaches a crosswalk. Compared to the actual pitchof the horn, the pitch observed by a pedestrian in thecrosswalk is

A) 15 cm B) 30 cm

C) 60 cm D) 120 cm

63. For a given sound wave, the total distance of 4compressions and 4 rarefactions is 120 centimeters.The wavelength of this sound wave is

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A) B)

C) D)

64. Which graph best represents the relationship betweenwavelength and frequency for sound waves?

A) radio wave B) microwave

C) light wave D) mechanical wave

65. Which type of wave requires a material mediumthrough which to travel?

A) decreases B) increases

C) remains the same

66. As the temperature of the air increases, the time ittakes for a sound wave to travel 20 meters

Base your answer to the following question on thegraph below which shows the variations in the speedof sound in air at different temperatures.

A) 6 m/s B) 10 m/s

C) 344 m/s D) 350 m/s

67. When the temperature of the air increases from 20ºCto 30ºC, the increase in the speed of sound is

A) 326 m/s B) 332 m/s

C) 344 m/s D) 350 m/s

68. What is the speed of sound in air on a day when thetemperature is 30ºC?

A) decreases B) increases

C) remains the same

69. As the temperature of air increases, the speed of soundin air

A) 0.453 s B) 2.21 s

C) 410. s D) 2.55 × 105 s

70. A person observes a fireworks display from a safedistance of 0.750 kilometer. Assuming that soundtravels at 340. meters per second in air, what is thetime between the person seeing and hearing thefireworks explosion?

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