# 7. Sound Waves

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does not travel through a vacuum In gases and liquids, primarily longitudinal waves In solids, can have transverse and longitudinal components Vibrations in fluids produce alternating high-pressure regions (called condensations) and low pressure regions (called refraction)

As disturbance reach the ear, the eardrum is set into vibration with pressure vibrations. On the other side of the ear drum, tiny bones (hammer, anvil and stirrup) carry the vibrations to the inner ear, where they are picked up by the auditory nerve

Characteristics of ear limit the perception of sound. Audible range for normal human ear is 20 Hz 20,000 Hz Infrasonic, if f < 20 Hz Example: Waves generated by wind and weather patterns, aircrafts, automobiles, longitudinal waves generated by earthquakes Can be perceived by elephants and cattle Ultrasonic, if f > 60,000 Hz Example: Those generated by high frequency vibrations in crystals Can be heard by dogs, cats and bats

Ultrasound is used in sonars, in medical diagnosis and in ultrasonic baths. Energy of sound is very small energy of 40,000 people shouting is equivalent to the energy for a 40-W bulb

Speed of sound Sound travels fastest in solids, least in gases In thin solid rods, In fluids,Y v ! V

v !

B V

K RT in ideal gases v ! MW

At STP, speed in air, v = 331 m/s = 1,087 ft/s

This is approximately 1 km } 1 mi 3 s 5h Used to estimate how far away lighting has struck by counting the no. of sec between the times you see the flash and you hear the thunder. At temperature,tc, At temperature, tF, v = 331 + 0.61 tc m/s ft/s v = 1,087 + 1.1(tf 32)

Speed of sound in materials at 00C and 1 atm unless otherwise noted.Medium Air Air (20 0C) Helium Hydrogen Mercury (25 0C) Water (25 0C) Seawater (25 0C) V, m/s Medium 331 343 972 1284 1450 1493 1533 Muscle (37 0C) Lead Concrete Copper Pyrex glass Aluminum Steel V, m/s 1580 1322 3100 3560 5640 5790 5790

Exercises2/443 Dolphins emit ultrasonic waves with a frequency as high as 2.5 x 105 Hz. What is the wavelength of such a wave in seawater at 25 0C? 4/443 Stan and Ollie hears standing next to a train track. Stan puts his ear to the steel track to hear the train coming. He hears the sound of the train whistle through the track 2.1 sec before Ollie hears it through the air. How far away is the train?

8/443 A copper alloy has Y = 1.1 x 1011Pa and a density of 8,920 kg/m3. what is the speed of sound in a thin rod made from this alloy? 10/444. A lightning flash is seen in the sky and 8.2 s later the boom of the thunder is heard. The temperature of the air is 12 0C. a. What is the speed of sound at that temperature? Hint: light is an EM wave with c = 3 x 10 8 m/s b. How far away is the lightning strike?

Intensity if SoundP I! A !1 [ BKA2 2

!

1 2

v 2 B V[ A ! Pmax 2B2 2

2 Pmax ! 2v V

Variation with distance from point source: I! P 4T R2

p

I1 ! I2

2 R2 2 R1

Intensity Level of Sound Sound intensity is perceived by the ear as loudness On the average, the human ear can detect sound waves (at 1 kHz) with an intensity as low as 10 12 W/m2. This is called the threshold of hearing, I0 . At an intensity of 1 W/m2, the sound is uncomfortably loud and may be painful to the ear. This is called the threshold of pain, Ip Intensity level in decibel,,

d F ! 10 log10

I I0

Intensity level, dB 180 140 120 110 100 90 80 70 60 50 40 20 0

Source of sound Rocket launch Jet take-off Pneumatic drill Rock band with amplifiers Machine shop Subway train Average factory City traffic Normal conversation Average home Quiet library Soft whisper Threshold of hearing

Remarks

Threshold of pain

Exposure to sounds over 90 dB for long periods may affect hearing

Exercises11/444 . A sound with an intensity level of 80 dB is incident on an eardrum of area 0.6 x 10-4 m2. how much energy is absorbed by the eardrum in 3.0 minutes?12/444 The sound level 25 m from a loudspeaker is 71 dB. What is the rate at which sound energy is produced by the loudspeaker, assuming it to be an isotropic source?

50/507 Cutnell A rocket in fireworks display explodes high in the air. The sound spreads out uniformly in all directions. The intensity of sound is 2 x 10 6 W/m2 at a distance of 120 m from the explosion. Find the distance from the source at which the intensity is 0.8 x 10 6 W/m2. 56/507 Two sources of sound are located on the x-axis, and each emits power uniformly in all directions. There are no reflections. One source is positioned a the origin and the other at x = +123 m. The source at the origin emits 4 times as much power as the other source. Where on the x-axis are the 2 sounds equal in intensity? Note that there are 2 answers.

14/444 Text At a race track. One race car starts its engine with a resulting intensity level of 98 dB. Then seven more cars start their engines. If the other seven cars produce the same intensity level as the first car, what is the new intensity level with all eight cars running at the starting line? 18/444 Text At a rock concert, the engineer decides that the music isnt loud enough. He turns up the amplifiers so that the amplitude of the sound where youre sitting, increases by 50%. By what % does the a. intensity increase? b. Intensity level change?

64/507 Cutnell A loudspeaker is generating sound in a room. At a certain point, the sound waves coming directly from the speaker (without reflecting from the walls) create an intensity level of 75 dB. The waves reflected from the walls, create, by themselves, an intensity level of 72 dB at the same point. What is the total intensity level? Hint: the answer is not 147 dB.

Doppler Effect A variation in the perceived wave frequency due to the relative motion of source and observer.

1 s v0 v s v0 v fo ! fs ! 1 # vs v # vs v Where:

f s

v0 > 0 if the obserever is moving toward the source, < 0 if moving away from the source vs > 0 if the source is moving toward the observer, < 0 if away from the observer

vt v sin U ! ! v s t vs

vs Mach No., M ! v

As a plane accelerates to just break the sound barrier, an unusual cloud might form. The origin of this cloud is still debated.

Shock wave trails out to the sides and downward of supersonic aircrafts. When this pressure ridges passes over an observer on the ground, the large concentration of energy produces what is known as a sonic boom. There are two such booms because shock waves are formed at both ends of the aircraft.

Exercises35/445 An ambulance traveling at 44 m/s approaches a car heading in the same direction at a speed of 28 m/s. The ambulance driver has a siren sounding at 350 Hz. At what frequency does the driver of the car hear the siren? 38/445 A source of sound waves of frequency 1 kHz travels through air at 0.5 times the speed of sound. Find the frequency of the sound received by a stationary observer if the source moves a. Toward her b. Away from her

40/445 A child on a swing hears the sound of a whistle that is being blown directly in front of her. At the bottom of her swing she hears a higher pitch if shes moving toward the whistle, and a lower pitch if she is moving away from it. The higher pitch has a frequency that is 5 % higher than the lower pitch. What is the speed of the child at the bottom of the swing? 46/446 a plane is flying at supersonic speed at an elevation where the sped of sound is 322 m/s. The shock wave forms with an angle U=220 with the direction of motion of the plane. a. What is the Mach no. for this plane? b. How fast is the plane traveling?

Homework34/506, Cutnell The wavelength of a sound wave in air is 2.74 m at 20 0C. What is the wavelength of this sound wave in fresh water at 20 0C? Hint: the frequency sound is the same in both media. 40/506, Cutnell The sound wave travels as far in neon as it does in krypton in the same time interval. Both can be treated as ideal gases. The atomic mass of neon is 20.2 u and that of krypton is 83.8 u. The temperature of the krypton is 293 K. What si the temperature of neon?

30/505, Cutnell A bat emits a sound whose frequency is 91 kHz. The speed of sound in air at 20 0C is 343 m/s. Find the wavelength of sound if the air temperature is 35 0C. 32/506, Cutnell Have you ever listened for an approaching train by kneeling next to a railroad track and putting your ear to the rail? Youngs modulus for steel is 2 x 1011 N/m2, and the density of steel is 7860 kg/m3. On a day when the temperature is 20 0C, how many times greater is the speed of sound in the rail than in the air?

48/507, Cutnell A typical adult ear has a surface area of 0.0021 m2. The sound intensity during a normal conversation is about 3.2 x 10 6 W/m2 at the listeners ear. Assume that the sound strikes the surface of the ear perpendicularly. How much power is intercepted by the ear? 65/507, Cutnell Two identical rifles are shot at the same time, and the sound intensity level is 80 dB. What would be the sound intensity level if only one rifle were shot? Hint: The answer is not 40 dB.

60/507 Cutnell A recording engineer works in a sound-proofed room that is 44 dB quieter than the outside. If the sound intensity in the room is 1.2 x 10 10 W/m2, what is the intensity outside? 58/507, Cutnell A middle-aged man typically has poorer hearing than a middle-aged woman. In one case a woman can just begin to hear a musical tone, while a man can just begin to hear the tone only when the intensity level is increased by 7.8 dB relative to that for the woman. What is the ratio of the sound intensity just detected by the man to that just detected by the woman?

70/507, Cutnell The security alarm on a parked car goes off and produces a frequency of 960 Hz. The speed

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