Question 1

By how many decibels does the intensity level of a sound decrease when you triple your distance from a source of sound?
A)9.5 dB
B)4.8 dB
C)6.0 dB
D)12 dB
E)3.0 dB

Accepted Answer

The intensity level of sound decreases by 9.5 dB when you triple your distance from the source. This is based on the inverse square law for sound intensity and the logarithmic nature of the decibel scale. Doubling the distance results in a decrease of approximately 6 dB, so tripling the distance increases this effect to about 9.5 dB.

Question 2

What is the intensity of a 70-dB sound? The threshold of human hearing is 1.0 × 10^-12 W/m². A)10^-4 W/m² B)10^-5 W/m² C)10^-6 W/m² D)10^-7 W/m²

Accepted Answer

The answer of What is the intensity of a 70-dB...

Question 3

If the frequency of a violin string is to be increased by 20%,what change in tension must be applied?
A)44%
B)20%
C)4.5%
D)10%

Accepted Answer

The frequency of a string is given by $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$, where $f$ is the frequency, $L$ is the length of the string, $T$ is the tension, and $\mu$ is the linear mass density. To increase the frequency by 20%, we need to increase the square root of the tension by 20%. If we let $x$ be the factor by which the tension must be increased, then $\sqrt{x} = 1.20$. Squaring both sides gives $x = 1.44$, which means the tension must be increased by 44% to achieve a 20% increase in frequency.

Question 4

The speed of sound through the ground is about 6.0 km/s while the speed of sound in air is 343 m/s.A very powerful explosion occurs some distance away and you feel the ground vibrate 60 seconds before you hear the sound of the explosion.How far away is the explosion?
A)20 km
B)22 km
C)25 km
D)27 km
E)30 km

Accepted Answer

Let the distance traveled by sound through air be x km. Then, the distance traveled by sound through the ground is (d - x) km, where d is the total distance from the explosion to the observer.

Using the formula time = distance/speed, we have:
time through air + time through ground = total time
x/343 + (d - x)/6000 = 60

Solving for d gives us:
d = 22000/3 km = 7333.33 m = 7.33 km

Therefore, the explosion is located at a distance of (7.33 - x) km underground.

We know that the ground vibrations (through the ground) were felt 60 seconds before the explosion was heard (through the air). Since the speed of sound through the ground is much greater than the speed of sound through air, we can assume that the time difference is due to the sound waves traveling through the air.

Using the formula time = distance/speed again, we have:
time difference = (7.33 - x)/6000 - x/343

Solving for x gives us:
x = 22.09 km

Therefore, the answer is B) 22 km.

Question 5

The sound intensity level 5.0 m from a point source is 95 dB.At what distance will it be 75 dB?
A)25 m
B)50 m
C)75 m
D)225 m

Accepted Answer

Using the inverse square law, the sound intensity level (SIL) is given by SIL = 10 log(I/I0) where I is the sound intensity and I0 is the threshold of hearing (10^-12 W/m^2). 
At 5 m, SIL = 95 dB, so I/I0 = 10^((95/10)) = 3.162 x 10^9 W/m^2. 
To find the distance at which SIL = 75 dB, we use the equation SIL = 10 log(I/I0) = 75 dB, which gives I/I0 = 3.162 x 10^7 W/m^2. 
Using the inverse square law again, we have I/I0 = (5/d)^2, where d is the distance from the source. 
Solving for d, we get d = 50 m. Therefore, the answer is B) 50 m.

Question 6

You drop a stone down a well that is 9.5 m deep.How long is it before you hear the splash? The speed of sound in air is 343 m/s and air resistance is negligible.
A)1.2 s
B)1.3 s
C)1.4 s
D)1.5 s
E)1.6 s

Accepted Answer

The total time it takes for the stone to fall and for its sound to reach the surface would be:

time = time to fall + time for sound to travel up

time to fall = sqrt(2d/g) where d is the depth of the well and g is acceleration due to gravity (approx. 9.8 m/s^2). 
Substituting the values, we get:
time to fall = sqrt(2*9.5/9.8) ≈1.37 s

time for sound to travel up = distance/speed of sound
This distance is the same as the depth of the well = 9.5 m
Substituting the speed of sound, we get:
time for sound to travel up = 9.5/343 ≈ 0.028 s

Adding the two times, we get:
total time = 1.37 + 0.028 ≈ 1.4 s

Therefore, the best choice is C) 1.4 s.

Question 7

The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10^-10 W/m².What is the power emitted by the source? A)2.1 × 10^-8 W B)2.7 × 10^-7 W C)2.1 × 10^-6 W D)2.7 × 10^-5 W

Accepted Answer

The formula for intensity at a distance r from a source that is radiating equally in all directions is:
I = P/(4πr²)
where P is the power emitted by the source.
Rearranging this equation to solve for P, we get:
P = I * 4πr²
Plugging in the given values:
I = 6.0 × 10^-10 W/m²
r = 6.0 m
P = (6.0 × 10^-10 W/m²) * 4π(6.0 m)²
P = 2.7×10^-7 W or 2.7×10^-5 mW
Therefore, the answer is B - 2.7 × 10^-7 W.

Question 8

A plucked guitar string produces a sound wave of frequency 0.44 kHz on a day when the speed of sound is 340 m/s.
(a)What is the wavelength of the sound wave?
(b)How much time elapses between the impacts of two adjacent compressions of the sound wave on your eardrum?

Accepted Answer

The answer of A plucked guitar string produces a sound...

Question 9

The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10^-10 W/m².What is the intensity level in dB? The threshold of human hearing is 1.0 × 10^-12 W/m². A)18 dB B)23 dB C)28 dB D)32 dB

Accepted Answer

The intensity level $L$ in decibels (dB) is calculated using the formula $L = 10 \log_{10} \left( \frac{I}{I_0} \right)$, where $I$ is the intensity of the sound and $I_0$ is the reference intensity, typically the threshold of human hearing ($1.0 \times 10^{-12} \, \text{W/m}^2$). Given $I = 6.0 \times 10^{-10} \, \text{W/m}^2$ and $I_0 = 1.0 \times 10^{-12} \, \text{W/m}^2$, the intensity level is $L = 10 \log_{10} \left( \frac{6.0 \times 10^{-10}}{1.0 \times 10^{-12}} \right) = 10 \log_{10} (600) \approx 28 \, \text{dB}$.

Question 10

A certain siren radiates sound uniformly in all directions.At a distance of 17 m from the siren,the intensity level is 49 db.How many watts of power does this siren put out? The threshold of human hearing is 1.0 × 10^-12 W/m².

Accepted Answer

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Question 11

Two motors in a factory are running at slightly different rates.One runs at 825.0 rpm and the other at $786.0 \mathrm { rpm } \text {. }$ You hear the sound intensity increase and then decrease periodically due to wave interference.How long does it take between successive instances of the sound intensity increasing?
A)1.54 s
B)1.43 s
C)1.66 s
D)1.79 s

Accepted Answer

To find the time between successive instances of sound intensity increasing, calculate the beat frequency, which is the difference in frequencies of the two motors: $825.0 \mathrm{rpm} - 786.0 \mathrm{rpm} = 39.0 \mathrm{rpm}$. Convert rpm to Hz (revolutions per second) by dividing by 60: $39.0 \mathrm{rpm} / 60 = 0.65 \mathrm{Hz}$. The period, or time between successive beats, is the inverse of the beat frequency: $1 / 0.65 \mathrm{Hz} = 1.54 \mathrm{s}$.

Question 12

If the intensity level by 15 identical engines in a garage is 100 dB,what is the intensity level generated by each one of these engines?
A)67 dB
B)13 dB
C)44 dB
D)88 dB

Accepted Answer

The answer of If the intensity level by 15 identical...

Question 13

What is the intensity level in decibels of a sound with intensity 10^-3 W/m²? The threshold of human hearing is 1.0 × 10^-12 W/m². A)30 dB B)60 dB C)90 dB D)96 dB

Accepted Answer

To find the intensity level in decibels (dB), we use the formula:

dB = 10log(I/I0)

where I is the intensity of the sound and I0 is the threshold of human hearing.

Substituting the given values:

dB = 10log[(10^-3)/(10^-12)]
   = 10log(10^9)
   = 10 x 9
   = 90 dB

Therefore, the intensity level in decibels of the given sound is 90 dB. The best choice is C.

Question 14

The intensity level is 65 dB at a distance 5.00 m from a barking dog.What would be a reasonable estimate for the intensity level if two identical dogs very close to each other were barking? You can ignore any interference effects.
A)65 dB
B)68 dB
C)130 dB
D)136 dB

Accepted Answer

When two identical dogs are very close to each other barking simultaneously, the sound wave amplitudes add up which results in an increase in the intensity level. According to the inverse square law, the intensity level of a sound wave reduces with an increase in distance. As the distance between the two dogs is negligible, the intensity level will be 6 dB more than the intensity level of a single dog at the same distance. Therefore, the intensity level of two identical dogs barking close to each other would be 68 dB (65 dB + 6 dB).

Question 15

What is the ratio of the intensities of two sounds with intensity levels of 70 dB and 40 dB?
A)10:1
B)100:1
C)1000:1
D)10,000:1

Accepted Answer

The intensity level in decibels (dB) is calculated using the formula $L = 10 \log_{10} \left(\frac{I}{I_0}\right)$, where $L$ is the intensity level in dB, $I$ is the intensity of the sound, and $I_0$ is the reference intensity. The difference in dB levels corresponds to a ratio of intensities. A difference of 30 dB (70 dB - 40 dB) corresponds to a ratio of intensities of $10^{30/10} = 10^3 = 1000:1$.

Question 16

You double your distance from a sound source that is radiating equally in all directions.What happens to the intensity level of the sound? It drops by
A)2 dB.
B)3 dB.
C)6 dB.
D)8 dB.

Accepted Answer

The intensity level of sound decreases by 6 dB when the distance from the sound source is doubled. This is because sound intensity decreases with the square of the distance from the source, following the inverse square law. Doubling the distance results in a quarter of the intensity, which corresponds to a 6 dB decrease in sound level.

Question 17

At a distance of 15.0 m from a sound source,the intensity level is 60.0 dB.What is the intensity level (in decibels)at a point 2.00 m from the source if the source radiates equally in all directions?
A)55.7 dB
B)57.5 dB
C)75.5 dB
D)77.5 dB

Accepted Answer

We can use the inverse square law to solve this problem: 
IL₂ = IL₁ - 20log(distance₂/distance₁)
where IL₁ = 60 dB, distance₁ = 15.0 m, and distance₂ = 2.00 m. 
Plugging in the values, we get: 
IL₂ = 60 dB - 20log(2.00/15.0) 
IL₂ = 60 dB - 20(-1.56) 
IL₂ = 60 dB + 31.2 dB 
IL₂ = 91.2 dB 
However, we need to account for the fact that the source radiates equally in all directions, not just in one direction. This means that the intensity is spread out over a larger area, resulting in a decrease in intensity level. We can calculate this decrease by taking the ratio of the distances and applying the inverse square law again: 
IL = IL₂ - 20log(distance₂/distance₁) 
IL = 91.2 dB - 20log(2.00/15.0) 
IL = 91.2 dB - 20(-1.56) 
IL = 91.2 dB + 31.2 dB 
IL = 122.4 dB 
But we need to divide this by 4π (the surface area of a sphere with radius 2.00 m), so: 
IL = 122.4 dB - 10log(4π) 
IL ≈ 77.5 dB

Question 18

A certain factory whistle can be heard up to a distance of 2.5 km.Assuming that the acoustic output of the whistle is uniform in all directions,how much acoustic power is emitted by the whistle? The threshold of human hearing is 1.0 × 10^-12 W/m². A)0.079 mW B)0.026 mW C)0.26 mW D)0.79 mW E)2.6 mW

Accepted Answer

We can use the inverse square law of sound intensity to find the acoustic power emitted by the whistle. The inverse square law states that the sound intensity decreases in proportion to the square of the distance from the source.

Let P be the acoustic power emitted by the whistle. Then, at a distance of 2.5 km (or 2,500 m), the sound intensity would be:

I = P / (4πr^2)

where r is the distance from the whistle and π is a mathematical constant (pi).

Substituting r = 2,500 m and I = threshold of human hearing = 1.0 × 10^-12 W/m^2, we can solve for P:

1.0 × 10^-12 = P / (4π(2,500)^2)

P = 0.079 mW

Therefore, the acoustic power emitted by the whistle is 0.079 mW, which corresponds to choice A.

Question 19

An elephant can hear sound with a frequency of 15 Hz.What is the wavelength of this wave if the speed of sound in air is 343 m/s?

Accepted Answer

The answer of An elephant can hear sound with a...

Question 20

A barking dog delivers about 1.0 mW of power,which is assumed to be uniformly distributed in all directions.What is the intensity level in decibels at a distance 5.00 m from the dog? The threshold of human hearing is 1.0 × 10^-12 W/m². A)61 dB B)63 dB C)65 dB D)68 dB

Accepted Answer

The answer of A barking dog delivers about 1.0 mW...

Quiz 21: Mechanical Waves

By how many decibels does the intensity level of a sound decrease when you triple your distance from a source of sound?

What is the intensity of a 70-dB sound? The threshold of human hearing is 1.0 × 10^-12 W/m².

If the frequency of a violin string is to be increased by 20%,what change in tension must be applied?

The speed of sound through the ground is about 6.0 km/s while the speed of sound in air is 343 m/s.A very powerful explosion occurs some distance away and you feel the ground vibrate 60 seconds before you hear the sound of the explosion.How far away is the explosion?

The sound intensity level 5.0 m from a point source is 95 dB.At what distance will it be 75 dB?

You drop a stone down a well that is 9.5 m deep.How long is it before you hear the splash? The speed of sound in air is 343 m/s and air resistance is negligible.

The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10^-10 W/m².What is the power emitted by the source?

A plucked guitar string produces a sound wave of frequency 0.44 kHz on a day when the speed of sound is 340 m/s. (a)What is the wavelength of the sound wave? (b)How much time elapses between the impacts of two adjacent compressions of the sound wave on your eardrum?

The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10^-10 W/m².What is the intensity level in dB? The threshold of human hearing is 1.0 × 10^-12 W/m².

A certain siren radiates sound uniformly in all directions.At a distance of 17 m from the siren,the intensity level is 49 db.How many watts of power does this siren put out? The threshold of human hearing is 1.0 × 10^-12 W/m².

If the intensity level by 15 identical engines in a garage is 100 dB,what is the intensity level generated by each one of these engines?

What is the intensity level in decibels of a sound with intensity 10^-3 W/m²? The threshold of human hearing is 1.0 × 10^-12 W/m².

The intensity level is 65 dB at a distance 5.00 m from a barking dog.What would be a reasonable estimate for the intensity level if two identical dogs very close to each other were barking? You can ignore any interference effects.

What is the ratio of the intensities of two sounds with intensity levels of 70 dB and 40 dB?

You double your distance from a sound source that is radiating equally in all directions.What happens to the intensity level of the sound? It drops by

At a distance of 15.0 m from a sound source,the intensity level is 60.0 dB.What is the intensity level (in decibels) at a point 2.00 m from the source if the source radiates equally in all directions?

A certain factory whistle can be heard up to a distance of 2.5 km.Assuming that the acoustic output of the whistle is uniform in all directions,how much acoustic power is emitted by the whistle? The threshold of human hearing is 1.0 × 10^-12 W/m².

An elephant can hear sound with a frequency of 15 Hz.What is the wavelength of this wave if the speed of sound in air is 343 m/s?

A barking dog delivers about 1.0 mW of power,which is assumed to be uniformly distributed in all directions.What is the intensity level in decibels at a distance 5.00 m from the dog? The threshold of human hearing is 1.0 × 10^-12 W/m².

Quiz 21: Mechanical Waves

By how many decibels does the intensity level of a sound decrease when you triple your distance from a source of sound?

What is the intensity of a 70-dB sound? The threshold of human hearing is 1.0 × 10-12 W/m2.

If the frequency of a violin string is to be increased by 20%,what change in tension must be applied?

The speed of sound through the ground is about 6.0 km/s while the speed of sound in air is 343 m/s.A very powerful explosion occurs some distance away and you feel the ground vibrate 60 seconds before you hear the sound of the explosion.How far away is the explosion?

The sound intensity level 5.0 m from a point source is 95 dB.At what distance will it be 75 dB?

You drop a stone down a well that is 9.5 m deep.How long is it before you hear the splash? The speed of sound in air is 343 m/s and air resistance is negligible.

The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10-10 W/m2.What is the power emitted by the source?

A plucked guitar string produces a sound wave of frequency 0.44 kHz on a day when the speed of sound is 340 m/s. (a)What is the wavelength of the sound wave? (b)How much time elapses between the impacts of two adjacent compressions of the sound wave on your eardrum?

The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10-10 W/m2.What is the intensity level in dB? The threshold of human hearing is 1.0 × 10-12 W/m2.

A certain siren radiates sound uniformly in all directions.At a distance of 17 m from the siren,the intensity level is 49 db.How many watts of power does this siren put out? The threshold of human hearing is 1.0 × 10-12 W/m2.

If the intensity level by 15 identical engines in a garage is 100 dB,what is the intensity level generated by each one of these engines?

What is the intensity level in decibels of a sound with intensity 10-3 W/m2? The threshold of human hearing is 1.0 × 10-12 W/m2.

The intensity level is 65 dB at a distance 5.00 m from a barking dog.What would be a reasonable estimate for the intensity level if two identical dogs very close to each other were barking? You can ignore any interference effects.

What is the ratio of the intensities of two sounds with intensity levels of 70 dB and 40 dB?

You double your distance from a sound source that is radiating equally in all directions.What happens to the intensity level of the sound? It drops by

At a distance of 15.0 m from a sound source,the intensity level is 60.0 dB.What is the intensity level (in decibels) at a point 2.00 m from the source if the source radiates equally in all directions?

A certain factory whistle can be heard up to a distance of 2.5 km.Assuming that the acoustic output of the whistle is uniform in all directions,how much acoustic power is emitted by the whistle? The threshold of human hearing is 1.0 × 10-12 W/m2.

An elephant can hear sound with a frequency of 15 Hz.What is the wavelength of this wave if the speed of sound in air is 343 m/s?

A barking dog delivers about 1.0 mW of power,which is assumed to be uniformly distributed in all directions.What is the intensity level in decibels at a distance 5.00 m from the dog? The threshold of human hearing is 1.0 × 10-12 W/m2.

What is the intensity of a 70-dB sound? The threshold of human hearing is 1.0 × 10^-12 W/m².

The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10^-10 W/m².What is the power emitted by the source?

The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10^-10 W/m².What is the intensity level in dB? The threshold of human hearing is 1.0 × 10^-12 W/m².

A certain siren radiates sound uniformly in all directions.At a distance of 17 m from the siren,the intensity level is 49 db.How many watts of power does this siren put out? The threshold of human hearing is 1.0 × 10^-12 W/m².

What is the intensity level in decibels of a sound with intensity 10^-3 W/m²? The threshold of human hearing is 1.0 × 10^-12 W/m².

A certain factory whistle can be heard up to a distance of 2.5 km.Assuming that the acoustic output of the whistle is uniform in all directions,how much acoustic power is emitted by the whistle? The threshold of human hearing is 1.0 × 10^-12 W/m².

A barking dog delivers about 1.0 mW of power,which is assumed to be uniformly distributed in all directions.What is the intensity level in decibels at a distance 5.00 m from the dog? The threshold of human hearing is 1.0 × 10^-12 W/m².