Question 1

A transverse wave is traveling in the -x direction on a string that has a linear density of 0.011 kg/m. The tension in the string is 7.4 N. The amplitude of the wave is 0.017 m; and its wavelength is 1.5 m. Which one of the following is the correct equation for the displacement of a particle from its equilibrium position?

Accepted Answer

The equation for the displacement of a particle in a transverse wave is given by y = Asin(kx - ωt), where A is the amplitude, k is the wave number, ω is the angular frequency, x is the position, and t is the time.

First, we need to find the wave number k and angular frequency ω. We know that the wavelength λ = 1.5 m and the speed of the wave v = √(T/μ), where T is the tension in the string and μ is the linear density of the string.

Using v = √(T/μ), we can solve for v:

v = √(7.4 N/0.011 kg/m) = 24 m/s

The wave number is given by k = 2π/λ = 4.19 rad/m, and the angular frequency is given by ω = 2πf, where f is the frequency of the wave.

To find the frequency, we can use the equation v = fλ, which gives us:

f = v/λ = 24/1.5 = 16 Hz

Therefore, ω = 2π(16 Hz) = 100.5 rad/s.

Now we can write the equation for the displacement of a particle:

y = Asin(kx - ωt)

Substituting the values we found, we get:

y = (0.017 m)sin(4.19x - 100.5t)

This matches choice B, so the answer is B.

Question 2

A bell is ringing inside of a sealed glass jar that is connected to a vacuum pump. Initially, the jar is filled with air. What does one hear as the air is slowly removed from the jar by the pump?

Accepted Answer

As the air is removed from the jar, the medium for sound transmission is reduced, causing the sound intensity to decrease.

Question 3

The Young's modulus of aluminum (density = 2700 kg/m³) is 6.9 × 10¹⁰ N/m². Determine the speed of sound in an aluminum rod.

Accepted Answer

The speed of sound in a material is given by:
v = sqrt(Y/ρ)
where Y is the Young's modulus and ρ is the density of the material. Substituting the given values, we get:
v = sqrt(6.9 × 10^10 N/m^2 / 2700 kg/m^3) = 5.1 × 10^3 m/s = 5.1 × 10^13 cm/s
Therefore, the answer is C, 5.1 × 10^3 m/s.

Question 4

A bell emits sound energy uniformly in all directions at a rate of 4.00 × 10^-³ W. What is the intensity of the wave 100.0 m from the bell?

Accepted Answer

The intensity of a wave is given by the formula I = P / (4πr²), where P is the power and r is the distance from the source. Substituting the given values, I = 4.00 × 10⁻³ W / (4π(100.0 m)²) = 3.18 × 10⁻⁸ W/m².

Question 5

Two fans are watching a baseball game from different positions. One fan is located directly behind home plate, 18.3 m from the batter. The other fan is located in the centerfield bleachers, 127 m from the batter. Both fans observe the batter strike the ball at the same time (because the speed of light is about a million times faster than that of sound), but the fan behind home plate hears the sound first. What is the time difference between hearing the sound at the two locations? Use 345 m/s as the speed of sound.

Accepted Answer

We can use the formula:

distance = speed x time

to find the time difference between the two locations. Let's call the time difference "t".

For the fan behind home plate:

distance = speed x time 
18.3 m = 345 m/s x t

Solving for t:

t = 18.3 m / 345 m/s 
t = 0.053 s

For the fan in the centerfield bleachers:

distance = speed x time 
127 m = 345 m/s x (t + X)

where "X" is the additional time it takes for the sound wave to travel the extra distance from home plate to centerfield.

Solving for X:

X = (127 m) / (345 m/s)
X = 0.368 s

Therefore, the time difference between hearing the sound at the two locations is:

t + X = 0.053 s + 0.368 s = 0.421 s - 0.053 s = 0.316 s

So the answer is A) 0.316 s.

Question 6

A transverse periodic wave is established on a string. The wave is described by the expression  where y is in meters when x and t are in meters and seconds, respectively. If the wave travels with a speed of 20.0 m/s, what is its frequency, f?

Accepted Answer

The answer of A transverse periodic wave is established on...

Question 7

When one person was talking in a small room, the sound intensity level was 60 dB everywhere within the room. Then, there were 14 people talking in similar manner simultaneously in the room, what was the resulting sound intensity level?

Accepted Answer

The sound intensity level increases by 10 dB when the number of identical sound sources increases tenfold. With 14 people, the increase is approximately 10*log10(14) ≈ 11 dB. Thus, the resulting level is 60 + 11 = 71 dB.

Question 8

A stationary railroad whistle is sounded. An echo is heard 5.0 seconds later by the train's engineer. If the speed of sound is 343 m/s, how far away is the reflecting surface?

Accepted Answer

The time it takes for the sound to travel to the reflecting surface and back is twice the time it took for the echo to be heard. Therefore, the total time for the sound to travel is 2 x 5.0 s = 10.0 s.

Using the equation distance = speed x time, we can calculate the distance between the train and the reflecting surface:

distance = 343 m/s x 10.0 s = 3430 m

However, that distance is the total distance traveled by the sound, so we need to divide it by 2 to get the distance to the reflecting surface:

distance to reflecting surface = 3430 m / 2 = 1715 m ≈ 860 m

Therefore, the reflecting surface is approximately 860 meters away from the train. The correct answer is (C).

Question 9

Castor oil has a density of 956 kg/m³. If the speed of sound in castor oil is 1474 m/s, what is its adiabatic bulk modulus?

Accepted Answer

The adiabatic bulk modulus can be calculated using the formula:

K = ρ * v^2 * γ

where ρ is the density, v is the speed of sound, and γ is the adiabatic index.

We have the density and speed of sound given in the problem, but we need to find γ. For castor oil, we can assume that it is a nearly incompressible fluid, so we can use the equation:

γ = Cp / Cv

where Cp is the specific heat at constant pressure and Cv is the specific heat at constant volume. For liquids, Cv is approximately equal to 3R, where R is the gas constant, and Cp is only slightly larger than Cv. We can use a value of γ = 1.35 for castor oil, which is typical for liquids.

Substituting the given values into the formula for K, we get:

K = 956 * (1474)^2 * 1.35
K ≈ 2.08 × 10^9 N/m^2

Therefore, the best choice is B.

Question 10

A physics student is asked to determine the length of a long, slender, copper bar by measuring the time required for a sound pulse to travel the length of the bar. The Young's modulus of copper is 1.1 × 10¹¹ N/m²; and its density is 8890 kg/m³. The student finds that the time for the pulse to travel from one end to the other is 5.6 × 10^-⁴s. How long is the rod?

Accepted Answer

The answer of A physics student is asked to determine...

Question 11

During a typical workday (eight hours), the average sound intensity arriving at Larry's ear is 1.8 × 10^-⁵ W/m². If the area of Larry's ear through which the sound passes is 2.1 × 10^-³ m², what is the total energy entering each of Larry's ears during the workday?

Accepted Answer

The total energy is calculated by multiplying the intensity by the area and the time: (1.8 × 10^-5 W/m^2) × (2.1 × 10^-3 m^2) × (8 hours × 3600 seconds/hour) = 1.1 × 10^-3 J.

Question 12

The speaker and two microphones shown in the figure are arranged inside a sealed container filled with neon gas. The wires from the microphones are connected to an oscilloscope (not shown). The signal from the microphones is monitored beginning at time t = 0 s when a sound pulse is emitted from the speaker. The pulse is picked up by microphone 1 at t₁ = 1.150 × 10^-² s and by microphone 2 at t₂ = 1.610 × 10^-² s. What is the speed of sound in neon gas?

Accepted Answer

The answer of The speaker and two microphones shown in...

Question 13

A guitar string is plucked and set into vibration. The vibrating string disturbs the surrounding air, resulting in a sound wave. Which entry in the table below is correct? wave in the string sound wave in air

Accepted Answer

The speed of sound waves in air increases with temperature, while the speed of waves in a string is not affected by air temperature.

Question 14

Two children setup a "telephone" by placing a long, slender aluminum (Y = 6.9 × 10¹⁰ N/m²) rod that has a length of 6.1-m between their two houses. To communicate, a child taps a coded message on one end. How long do the sound waves take to reach the other end? Note: the density of aluminum is 2700 kg/m³.

Accepted Answer

The speed of sound in a solid is given by v = sqrt(Y/p), where Y is Young's modulus and p is the density. Plugging in the given values, we get v = sqrt(6.9 × 10^10 N/m^2 / 2700 kg/m^3) = 5100 m/s. The time it takes for the sound waves to reach the other end is then t = d/v = 6.1 m / 5100 m/s = 1.2 × 10^-3 s.

Question 15

Two boys are whispering in the library. The radiated sound power from one boy's mouth is 1.2 × 10^-⁹ W; and it spreads out uniformly in all directions. What is the minimum distance the boys must be away from the librarian so that she will not be able to hear them? The threshold of hearing for the librarian is 1.00 × 10^-¹² W/m².

Accepted Answer

The intensity of the sound wave at a distance r from the source is given by:$$I = \frac{P}{4\pi r^2}$$where P is the power of the sound source. The threshold of hearing is the minimum intensity of sound that can be heard by a person. In this case, the threshold of hearing is 1.00 × 10^-12 W/m^2. We can use this to find the minimum distance the boys must be away from the librarian so that she will not be able to hear them:$$1.00 	imes 10^{-12} W/m^2 = \frac{1.2 	imes 10^{-9} W}{4\pi r^2}$$$$r^2 = \frac{1.2 	imes 10^{-9} W}{4\pi (1.00 	imes 10^{-12} W/m^2)}$$$$r = \sqrt{\frac{1.2 	imes 10^{-9} W}{4\pi (1.00 	imes 10^{-12} W/m^2)}} = 9.8 m$$Therefore, the minimum distance the boys must be away from the librarian so that she will not be able to hear them is 9.8 m.

Question 16

How far must one stand from a 5-mW point sound source if the intensity at that location is at the hearing threshold? Assume the sound waves travel to the listener without being disturbed.

Accepted Answer

The answer of How far must one stand from a...

Question 17

The decibel level of a jackhammer is 125 dB relative to the threshold of hearing. Determine the sound intensity produced by the jackhammer.

Accepted Answer

The answer of The decibel level of a jackhammer is...

Question 18

A transverse periodic wave on a string with a linear density of 0.200 kg/m is described by the following equation: y = 0.08 sin(469t - 28.0x), where x and y are in meters and t is in seconds. What is the tension in the string?

Accepted Answer

The wave equation for a transverse wave on a string is:

v = sqrt(T/μ)

where v is the wave speed, T is the tension in the string, and μ is the linear density of the string (mass per unit length).

We can find the wave speed from the equation:

v = λf

where λ is the wavelength and f is the frequency. The frequency is given by the equation:

f = ω/2π

where ω is the angular frequency. The angular frequency is given by the coefficient of t in the equation for y:

ω = 469

The wavelength is given by:

λ = 2π/k

where k is the wave number. The wave number is given by the coefficient of x in the equation for y:

k = 28.0

Substituting these values into the equations gives:

f = ω/2π = 469/2π ≈ 74.5 Hz

λ = 2π/k = 2π/28.0 ≈ 0.224 m

v = λf = 0.224 × 74.5 ≈ 16.7 m/s

Finally, we can use the wave speed and linear density to find the tension:

T = μv^2 = 0.200 × 16.7^2 ≈ 56.1 N

Therefore, the answer is C.

Question 19

The intensity of a spherical wave 2.5 m from the source is 120 W/m². What is the intensity at a point 9.0 m away from the source?

Accepted Answer

The intensity of a spherical wave decreases with the square of the distance from the source. Using the inverse square law: I2 = I1 * (r1/r2)^2 = 120 * (2.5/9)^2 = 9.3 W/m².

Question 20

The speed of sound in fresh water at 293 K is 1482 m/s. At what temperature is the speed of sound in helium gas the same as that of fresh water at 293 K? Helium is considered a monatomic ideal gas ($\gamma$ = 1.67 and atomic mass = 4.003 u).

Accepted Answer

The answer of The speed of sound in fresh water...

Quiz 16: Waves and Sound

A bell is ringing inside of a sealed glass jar that is connected to a vacuum pump. Initially, the jar is filled with air. What does one hear as the air is slowly removed from the jar by the pump?

The Young's modulus of aluminum (density = 2700 kg/m³) is 6.9 × 10¹⁰ N/m². Determine the speed of sound in an aluminum rod.

A bell emits sound energy uniformly in all directions at a rate of 4.00 × 10^-³ W. What is the intensity of the wave 100.0 m from the bell?

A transverse periodic wave is established on a string. The wave is described by the expression where y is in meters when x and t are in meters and seconds, respectively. If the wave travels with a speed of 20.0 m/s, what is its frequency, f?

When one person was talking in a small room, the sound intensity level was 60 dB everywhere within the room. Then, there were 14 people talking in similar manner simultaneously in the room, what was the resulting sound intensity level?

A stationary railroad whistle is sounded. An echo is heard 5.0 seconds later by the train's engineer. If the speed of sound is 343 m/s, how far away is the reflecting surface?

Castor oil has a density of 956 kg/m³. If the speed of sound in castor oil is 1474 m/s, what is its adiabatic bulk modulus?

During a typical workday (eight hours) , the average sound intensity arriving at Larry's ear is 1.8 × 10^-⁵ W/m². If the area of Larry's ear through which the sound passes is 2.1 × 10^-³ m², what is the total energy entering each of Larry's ears during the workday?

A guitar string is plucked and set into vibration. The vibrating string disturbs the surrounding air, resulting in a sound wave. Which entry in the table below is correct? wave in the string sound wave in air

How far must one stand from a 5-mW point sound source if the intensity at that location is at the hearing threshold? Assume the sound waves travel to the listener without being disturbed.

The decibel level of a jackhammer is 125 dB relative to the threshold of hearing. Determine the sound intensity produced by the jackhammer.

A transverse periodic wave on a string with a linear density of 0.200 kg/m is described by the following equation: y = 0.08 sin(469t - 28.0x) , where x and y are in meters and t is in seconds. What is the tension in the string?

The intensity of a spherical wave 2.5 m from the source is 120 W/m². What is the intensity at a point 9.0 m away from the source?

The speed of sound in fresh water at 293 K is 1482 m/s. At what temperature is the speed of sound in helium gas the same as that of fresh water at 293 K? Helium is considered a monatomic ideal gas ( $\gamma$ = 1.67 and atomic mass = 4.003 u) .

Quiz 16: Waves and Sound

A bell is ringing inside of a sealed glass jar that is connected to a vacuum pump. Initially, the jar is filled with air. What does one hear as the air is slowly removed from the jar by the pump?

The Young's modulus of aluminum (density = 2700 kg/m3) is 6.9 × 1010 N/m2. Determine the speed of sound in an aluminum rod.

A bell emits sound energy uniformly in all directions at a rate of 4.00 × 10-3 W. What is the intensity of the wave 100.0 m from the bell?

A transverse periodic wave is established on a string. The wave is described by the expression where y is in meters when x and t are in meters and seconds, respectively. If the wave travels with a speed of 20.0 m/s, what is its frequency, f?

When one person was talking in a small room, the sound intensity level was 60 dB everywhere within the room. Then, there were 14 people talking in similar manner simultaneously in the room, what was the resulting sound intensity level?

A stationary railroad whistle is sounded. An echo is heard 5.0 seconds later by the train's engineer. If the speed of sound is 343 m/s, how far away is the reflecting surface?

Castor oil has a density of 956 kg/m3. If the speed of sound in castor oil is 1474 m/s, what is its adiabatic bulk modulus?

During a typical workday (eight hours) , the average sound intensity arriving at Larry's ear is 1.8 × 10-5 W/m2. If the area of Larry's ear through which the sound passes is 2.1 × 10-3 m2, what is the total energy entering each of Larry's ears during the workday?

A guitar string is plucked and set into vibration. The vibrating string disturbs the surrounding air, resulting in a sound wave. Which entry in the table below is correct? wave in the string sound wave in air

How far must one stand from a 5-mW point sound source if the intensity at that location is at the hearing threshold? Assume the sound waves travel to the listener without being disturbed.

The decibel level of a jackhammer is 125 dB relative to the threshold of hearing. Determine the sound intensity produced by the jackhammer.

A transverse periodic wave on a string with a linear density of 0.200 kg/m is described by the following equation: y = 0.08 sin(469t - 28.0x) , where x and y are in meters and t is in seconds. What is the tension in the string?

The intensity of a spherical wave 2.5 m from the source is 120 W/m2. What is the intensity at a point 9.0 m away from the source?

The speed of sound in fresh water at 293 K is 1482 m/s. At what temperature is the speed of sound in helium gas the same as that of fresh water at 293 K? Helium is considered a monatomic ideal gas ( γ\gammaγ = 1.67 and atomic mass = 4.003 u) .

The Young's modulus of aluminum (density = 2700 kg/m³) is 6.9 × 10¹⁰ N/m². Determine the speed of sound in an aluminum rod.

A bell emits sound energy uniformly in all directions at a rate of 4.00 × 10^-³ W. What is the intensity of the wave 100.0 m from the bell?

Castor oil has a density of 956 kg/m³. If the speed of sound in castor oil is 1474 m/s, what is its adiabatic bulk modulus?

During a typical workday (eight hours) , the average sound intensity arriving at Larry's ear is 1.8 × 10^-⁵ W/m². If the area of Larry's ear through which the sound passes is 2.1 × 10^-³ m², what is the total energy entering each of Larry's ears during the workday?

The intensity of a spherical wave 2.5 m from the source is 120 W/m². What is the intensity at a point 9.0 m away from the source?

The speed of sound in fresh water at 293 K is 1482 m/s. At what temperature is the speed of sound in helium gas the same as that of fresh water at 293 K? Helium is considered a monatomic ideal gas ( $\gamma$ = 1.67 and atomic mass = 4.003 u) .