Chapter 12 Sound

The softest sound that the average human can hear is

1 x 10^-12 W/m^2

Intensity that causes perforation of the eardrum is

1 x 10^4 W/m^2

Every time we divide by 10, we subtract _______ from B

10

Every time we multiply by 10, we add ______ to B

10

The intensity of sound at the threshold of pain is

10 W/m^2

Two transverse waves with identical frequencies interfere, creating a resulting wave with amplitude 8 cm. If one of the original waves has amplitude 12 cm, then the other wave's amplitude could be any of the following EXCEPT: A. 3 cm B. 4 cm C. 12 cm D. 20 cm

A

A man standing 1m away from an omnidirectional speaker is exposed to a sound of 140 dB. How far would he have to travel in order to no longer be in pain (120 dB), given I = P/A and B = 10 log (I/I0) where I0 A. 9m B. 10m C. 20m D. 100m

A To decrease by 20 dB, you need to decrease r by a factor of 10 This is a distance of 10m, but since you are already 1 m away, the answer is 9m

What is the Doppler effect?

A change in sound frequency caused by motion of the sound source, motion of the listener, or both.

A guitar string is playing notes that are flat (frequency too low). How can the string be made to play the correct notes? A. Increase the tension in the string to increase the wave speed B. Increase the tension in the string to decrease the wavelength C. Decrease the tension in the string to increase the wave speed D. Decrease the tension in the string to decrease the wavelength

A;

A person listening to music on a stereo system experiences a sound level of 70 dB. If the volume dial is turned up to increase the intensity by a factor of 500, what sound level would this person hear now? A. 97 dB B. 105 dB C. 115 dB D. 120 dB

A;

A siren produces sound waves in the air. If the frequency of the waves is gradually decreasing, which of the following changes to the waves is most likely also occurring? A. The wavelength is increasing B. The wave speed is decreasing C. The amplitude is decreasing D. The period is decreasing

A;

The engine of a small and unmanned airplane produces a known and specific sound frequency (not given). A stationary sound detection device observes that the known emitted frequency is 90% of the perceived sound frequency. Relative to the detection to the device in which direction and at what velocity is the plane moving A. Towards the detector at 34 m/s B. Away the detector at 34 m/s C. Towards the detector at 64 m/s D. Away the detector at 64 m/s

A; The prompt stated that the emitted sound frequency (fs) is 90% of the perceived sound frequency (fD), therefore fD/fS = 10/9

A piano tuner strikes a tuning fork at the same time he strikes piano key with a node of a similar pitch. If he hears 3 beats per second, and the tuning fork produces a standard 440 Hz tone, then what must be the frequency produced by the struck piano string? A. 437 Hz B. 443 Hz C. 437 or 443 Hz D. 434 or 446 Hz

C;

A herpetologist studying alligators at the Kennedy Space center is 1000m from the launch pad, when a siren sounds, signaling 30 minutes to launch. After running away for 4000m, the herpetologist turns to watch the launch. How does the intensity of sound produced by the siren at his new location compare to the original intensity, I, given I = P/A A. 5 I B. 1/5 I C. 1/25 I D. 1.50 I

C; New r is 5 times the original A is proportional to r^2 A = 25 I = 1/25

A 37.5 cm glass pipe that is open at both ends is placed next to a student a cappella group. It was observed that the pipe first resonates when the choir produces a note at 450 Hz. At which subsequent frequencies will resonate again be observed? (the speed of sound through a pipe is 350 m/s) A. 675 Hz and 900 Hz B. 675 Hz and 1350 Hz C. 900 Hz and 1350 Hz D. 900 Hz and 1800 Hz

C; f beat = |f1-f2| 450 = |f1-f2| C has the only values that work

A fire truck's siren emits a sound with frequency 990 Hz. It moves toward a stationary observer with a speed of 35 m/s, passes the observer, then moves 35 m/s away from the observer. What is the difference between the frequencies measured by the observer before and after the truck passes? (The speed of sound in air is approximately 350 m/s.) A. 100 Hz B. 110 Hz C. 200 Hz D. 220 Hz

C; f' = f (v +- vd / v-+ vs) f' = 990 Hz (350 / 350 - 35) f' = 990 (350/315) f' = 1100 Hz f' = 990 Hz (350 / 350 + 35) f' = 990 Hz (350 / 385) f' = (990 Hz) (10/11) f' = 900 Hz 1100 - 900 = 200 Hz

A string attached at each end is vibrating in its 4th harmonic mode. If the distance between each node and its closest antinode is 40 cm, then what is the length of the string? A. 1.6 m B. 2.4 m C. 3.2 m D. 6.4 m

C; When a string vibrates in its 4th harmonic mode, it means that there are 4 half-wavelengths (i.e. 2 full wavelengths) along the length of the string. The distance between a node and the closest antinode is one quarter of a wavelength, so λ = 4(40 cm) = 160 cm or 1.6 m. The length of string is therefore 2λ = 3.2 m.

A standing wave is created in a 6 m string attached at each end. If the distance between consecutive nodes is 0.5 m, then the string is vibrating in its: A. third harmonic mode. B. sixth harmonic mode. C. twelfth harmonic mode. D. Cannot be determined with the information given.

C; When a string vibrates in its nth harmonic mode, it means there are n half-wavelengths along the length of the string. Since the distance between consecutive nodes is one half of a wavelength, then there must be (6 m) / (0.5 m) = 12 half-wavelengths, and therefore n = 12.

What are shockwaves?

Highly contended waves that cause physical disturbances as it passes through objects

What happens to the sound level intensity when it decreases by 90 %

I - 90% = 1/10 its original value I goes down by 10 dB

Intensity equation (for sound)

I = P/A I = intensity (Watt/m^2) P = power (W) A = m^2

Intensity is proportional to A how?

I = proportional to A^2

A speaker emitting a sound with a constant frequency approaches a detector. Which of the following characteristics will have a greater value at the detector than at the source? I. Frequency II. Wavelength III. Speed

I only

What is the length of a closed pipe in the third harmonic?

L = 3y/4

What is the length of an open pipe in the third harmonic

L = y

What is the length of the closed pipe in the firsts harmonic?

L = y/4

What are open pipes?

Pipes that are open at both ends

What is damping of sound?

Real world measurements sounding lower than expected calculations

What is ultrasound?

Sound waves beyond the range of human hearing - 20,000Hz

What are beats?

Two almost identical tones combined in rapid fluctuation in amplitude.

What happens to the sound level intensity when it Increases by a factor of 100?

Up 20dB

What happens when the sound level intensity goes up by a factor of 30?

Up by 10-20 bB

What are longitudinal waves?

Waves that move in the same direction as the wave (parallel)

What is resonance?

When an object is forced to vibrate at its natural frequency

What is a sonic boom?

When the passing of a shock wave creates high pressure, followed by low pressure.

Frequency of a closed pipe equation

f = nv/4L

If a car horn sounds a pitch of 1400 Hz and the car is driving up behind you on the freeway at 40 m/s while you creep along at 10 m/s in the same direction, what pitch will you hear? Use v(sound) = 340 m/s

f' = 1540 Hz

Doppler effect equation

f' = f (V +/- Vd)/ (V -/+ Vs) where V = speed of sound in the medium Vd = speed of the detector Vs = speed of the source Top sign: toward (if source or detector is moving toward other) Bottom sign: away (if they moving away from other object) *Treat numerator and denominator separately when deciding if top or bottom sign

When all the finger holes on a clarinet are closed, it can be approximated as a hollow tube with one closed end (mouthpiece) and an open end. When all the finger holes on a clarinet are closed, the lowest pitch that can be produced corresponds to the G-flat below middle C (185 Hz). How long is the clarinet? Assume the speed of sound in air is 340 m/s A. 90 cm B. 70 cm C. 45 cm D. 30 cm

f1 = v/4L L = v/4f L = 340 / (4)(185) L = .5m or about 45 cm

Beat frequency equation

fbeat = |f1 - f2|

Damping does not have an affect on _________

frequency

Sound travels slowest through which medium?

gas

The distance between displacement antinodes is equal to a whole number of _______ wavelengths

half

Intensity varies _________ as the _______ of the distance r from the source

inversely; distance

Sound waves are what type of wave?

longitudinal

Glass shatters when a sound produced matches its ________ frequency

natural

In the case of the closed pipe, the closed end corresponds to a

node

The closed end of a pipe corresponds to a

node

As a shortcut for open pipes, the number of _______ present will tell you which harmonic

nodes

Because the closed end must always have a node and mist always have an antinode, there can only be _______ numbered harmonics

odd

The harmonic in a closed pipe is equal to the number of _______ wavelengths

quarter

The ________ harmonic (first overtone) of an open pipe has a wavelength equal to the length of the pipe.

second

Sound travels fastest through which medium?

solid

What mediums can sound travel through?

solids, liquids, and gases

What is intensity of sound?

the rate at which a wave's energy flows through a given area

Ultrasound machines calculate distance based upon:

travel time of the reflected sound

When a longitudinal compression wave of frequency 700 Hz travels through a brass rod, its wavelength is 5m. How fast does sound travel through brass?

v = yf v = (5m)(700 Hz) v = 3500 m/s

What is the wavelength of a sound wave of frequency 170 Hz if the wave speed is 340 m/s?

v = yf y = v/f y = 340 m/s / 170 s^-1 y = 2m

What is the wavelength of an open pipe in the third harmonic?

y = 2L/3

What is the length of an open pipe in the third harmonic?

y = 2L/3 L = 3y/2

An organ pipe that is open at both ends has a length of 3m. What is the second longest harmonic wavelength for sound waves in this pipe. A. 3 m B. 4 m C. 6 m D. 9 m

y = 2L/n y = 2(3) / 2 y = 3m

What is the length of an open pipe in an open pipe?

y = 2L/n y = 2L/1 y = 2L L = y/2

What is the wavelength of an open pipe in the second harmonic?

y = 2L/n y = 2L/2 y = L

Wavelength for a closed pipe equation

y = 4L/n

What is the wavelength of the first harmonic of a closed pipe?

y = 4L/n y = 4L

What is the wavelength of a closed pipe in the third harmonic?

y = 4L/n y = 4L/3

What is the wavelength of the first harmonic of an open pipe?

y1 = 2L/1 = 2L

Nodes are also called

displacement nodes or pressure antinodes

A stationary cat is purring. Which of the following correctly explains why its owner hears a frequency that is higher than that which is produced by the cat? A. The owner is moving towards the cat B. The owner is moving away from the cat C. Both are on an accelerating train D. Both are on a decelerating boat

A

A string on a violin, vibrating at an unknown frequency, is played at the same time as another string vibrating at a frequency of 262 Hz. The beat frequency is 4 Hz. If the unknown string is known to be too low in pitch (musically flat), then at what frequency is it vibrating? A. 258 Hz B. 266 Hz C. 258 Hz or 266 Hz D. 258 Hz and 266 Hz

A; The beat frequency, fbeat, is given by fbeat = |f1 - f2| where f1 and f2 are the frequencies of the individual sound waves. Since the beat frequency is 4 Hz, and one of the sound frequencies is 262 Hz, the other frequency must either be 262 + 4 = 266 Hz or 262 - 4 or 258 Hz. Since the string is known to be flat, the frequency must be lower that 262 Hz, so choice A is correct. Note that choice D can be eliminated right away since the string cannot play both frequencies at once.

In the previous example, suppose you began 100m from the sound source. After moving closer, how far from the sound source are you? A. 10 m B. 1 m C. 1 cm D. .1 mm

B I is proportional to A^2 I is inversely proportional to r^2 r = 1/sqrt I r = 1/10^4 r = 1/100 or 10^-2 10^-2 x 10^2m = 1m

What is the intensity level of a sound wave?

B = 10 log 10 I/I0

An airplane traveling at 157 m/s north on a runway and is producing a sound of frequency f. A woman is seated in a car moving 43 m/s to the south, away from the airplane. What frequency will she observe (assume the speed of our is 343 m/s) A. 1/2 f B. 3/5 f C. f D. 2f

B;

Two speakers are emitting identical sound waves with frequency 170 Hz (the speed of sound is approximately 340 m/s). If a person stands 3 meters from one speaker and 4 meters from the other speaker, he will experience: A. constructive interference. B. destructive interference. C. beats. D. a Doppler shift.

B;

A pipe closed at one end supports a standing wave vibrating in its 3rd harmonic mode. If the closed end is then opened, and a standing wave is created with twice the previous frequency, then what is the pipe's new harmonic mode? A. 1.5 B. 3 C. 6 D. 12

B; A is wrong --> harmonics MUST be integers closed: f = nV/4L f = 3v/4L open: nv/2L (2)(3v)/4L = vn/2L v and L cancel (2)(3) / 4 = n/2 6/4 = n/2 n = 3

Suppose one moves 10 times further away from a loud siren of constant power. What is the resultant decrease in sound level? A. 10 dB B. 20 dB C. 40 dB D. 100 dB

B; I = P/A I = P/100 I = 1/100 1/100 is a decrease by 10^2, or 20 dB

If you move five times further away from the source of a sound, how does the amplitude of the pressure wave change? A. It does't B. It decreases by a factor of 5 C. It decreases by a factor of 25 D. It decreases by a factor of 125

B; I is inversely proportional to the square of the radius I = 1/25 Intensity is inversely proportional to the square root of A A = sqrt I A = sqrt 1/25 A = 1/5

An organ pipe that is closed at one end has a length of 3m. What is the second-longest harmonic wavelength for sound waves in this pipe? A. 3 m B. 4 m C. 6 m D. 9 m

B; y = 4L/3 y = 4(3)/3 y = 4m

A sound wave of frequency 440 Hz (this not is concert A, or A above middle C) travels at a speed of 344 m/s through the air in the concert hall. How fast would a note one octave higher, 880 Hz, travel through the same concert wall? A. 172 m/s B. 344 m/s C. 516 m/s D. 688 m/s

B; Altering the frequency will not affect the wave speed. Remember big rule 1 for waves. Therefore, the answer is B

A typical medical ultrasound scan uses frequencies in the MHz range. What would happen to an ultrasound signal as it passed from air into body tissues? A. Its wavelength and speed would decrease B. Its wavelength and speed would increase C. Its wavelength would decrease and its speed would increase D. Its wavelength would increase and its speed would decrease

B; When a wave passes into a new medium, its frequency does not change. Therefore, when traveling through the body, the frequency of the sound wave will be the same. However, we know that the sound waves generally travel faster through liquids and silos than they do through gases, so we'd expect the wave speed through the body to travel faster.

change in sound level equation

Bf = Bi + 10log(If/Ii)

At a distance of 1m, the intensity level of a soft whisper is about 30 dB, while a normal speaking voice is about 60 dB. How many times greater is the power delivered per unit area by a normal speaking vice than by a whisper? A. 2.5 B. 30 C. 1000 D. 3000

C

A pipe open at both ends supports a standing wave vibrating in its n = 5 harmonic mode. All of the following would decrease the frequency EXCEPT: A. using a longer pipe but keep n the same. B. using the same length pipe and decreasing n. C. closing one end of the pipe and keeping n the same. D. increasing the temperature of the air inside the pipe.

D

Moving closer to a sound source, you find that your received sound level increases from 20 dB to 60 dB. By how much did the sound's intensity increase? A. By 40 W/m^2 B. By a factor of 40 C. By a factor of 100 D. By a factor of 10,000

D

All of the following changes would LOWER the frequency played by a plucked string attached at each end EXCEPT: A. decreasing the tension in the string. B. using string with the same length but greater mass. C. using a longer string. D. decreasing the amplitude of oscillation.

D;

A person stands at an equal distance between two speakers which produce identical sound waves. If the person moves so that she is 1.5 m closer to one speaker than the other, she is in a "quiet zone" (i.e. the waves experience destructive interference). The wavelength of the sound waves could be all of the following EXCEPT: A. 0.6 m B. 1 m C. 3 m D. 6 m

D; If the path difference from two wave sources to the detector is an integer multiple of wavelengths, then the waves will experience constructive interference (i.e. compressions will line up with compressions, rarefactions will line up with rarefactions). This can be expressed as d2 - d1 = mλ, where d2 and d1 are lengths of the paths traveled by the waves, m is an integer and λis the wavelength. Similarly, if the path difference is equal to an integer-and-a-half times the wavelength, the waves will experience destructive interference: d2 - d1 = (m + 1/2)λ. Since the waves are experiencing destructive interference, 1.5 = (m + 1/2)λ. So 1.5 could equal λ / 2 or 3λ / 2 or 5λ / 2, etc. Solving for λ, we get that λ = 2(1.5) = 3 or (2/3)(1.5) = 1 or (2/5)(1.5) = 0.6, etc. (all answers in meters). Choice D is the only answer not possible.

Two transverse waves with identical frequencies interfere. If their amplitudes are 10 cm and 15 cm, respectively, what will be resulting amplitude? A. 12.5 cm B. 25 cm C. a value between 0 and 25 cm D. a value between 5 and 25 cm

D; The principle of superposition for waves states that, when two or more waves interfere, the resulting displacement from equilibrium is the sum of the individual displacements. The two extreme cases are 1) when the crests (and the troughs) line up, or 2) when the crest of one lines up with the trough of the other. In the first case, the amplitudes add: 10 cm + 15 cm = 25 cm. In the second case, the amplitudes subtract: 15 cm - 10 cm = 5 cm. Since these represent only the extreme cases, any amplitude between 5 cm and 25 cm is possible.

The open end of a pipe corresponds to a(n)

antinode

An open pipe has _________ at both ends

antinodes

For strings, the number of ________ tells you which harmonic

antinodes

The first harmonic in a closed pipe consists of only the node at the closed end and the _______ at the open end

antinodes

Shock waves are greatest when traveling ______ the speed of sound

at

Unit of intensity

bel (B), more commonly seen as decibel

As a stereo speaker, vocal folds or tuning fork vibrates, it creates regions of high pressure called _________ that alternate between regions of _______ pressure

compressions rarefactions

Anitnodes are also called

displacement antinodes or pressure nodes