Question 1

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?

Accepted Answer

The explosion's distance can be calculated by first determining the time it takes for the sound to travel through the ground and air. Given the speed of sound through the ground (6.0 km/s) and in air (343 m/s or 0.343 km/s), and knowing the ground vibration is felt 60 seconds before the sound is heard, we can set up an equation where the distance (d) is equal for both mediums but the time differs by 60 seconds. Let $ t $ be the time sound takes to travel through the air, then $ t - 60 $ seconds is the time for the ground. The equations are $ d = 6.0 \times (t - 60) $ for the ground and $ d = 0.343 \times t $ for the air. Equating and solving for $ t $ gives the time it takes for the sound to travel through the air, and subsequently, $ d $ can be calculated. Solving these equations yields a distance of approximately 22 km.

Question 2

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?

Accepted Answer

From the inverse square law of sound propagation, the intensity of sound decreases by a factor of $(15	ext{ m}/2.00 	ext{ m})^2 = 56.25$ times, since the distance from the source is reduced to $\frac{1}{7}$ of the initial value. Therefore, the intensity level at the new point is

$$60.0	ext{ dB} - 10\log_{10}(56.25) \approx 77.52	ext{ dB} \approx \boxed{77.5	ext{ dB}}$$

Note that choice (A) is close to the correct answer, but it is likely a result of rounding off the exact value of the logarithm, and thus not accurate enough. Choice (B) is too small compared to the initial level, and choice (C) is too large.

Question 3

What are the wavelength (in meters)and frequency (in hertz)of a wave whose displacement is given by the equation y = 0.5 sin(0.20x + 120t),where x and y are in meters and t is in seconds?

Accepted Answer

The answer of What are the wavelength (in meters)and frequency...

Question 4

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.

Accepted Answer

The intensity level in decibels (dB) can be calculated using the formula: $ \text{Level (dB)} = 10 \log_{10} \left( \frac{I}{I_0} \right) $, where $I$ is the intensity of the sound and $I_0$ is the reference intensity (threshold of human hearing), which is $1.0 \times 10^{-12} \, \text{W/m}^2$. Substituting $I = 6.0 \times 10^{-10} \, \text{W/m}^2$ and $I_0 = 1.0 \times 10^{-12} \, \text{W/m}^2$ into the formula gives $ \text{Level} = 10 \log_{10} (600) $, which calculates to approximately 28 dB.

Question 5

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.

Accepted Answer

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

Question 6

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?

Accepted Answer

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

Question 7

Light from a laser forms a 1.31-mm diameter spot on a wall.If the light intensity in the spot is 
What is the power output of the laser? Assume that all the light emitted by the laser hits the spot.

Accepted Answer

The intensity I of light is given by the formula:
I = P/A, where P is the power and A is the area that the light is spread over.
In this case, we have I = 11 × 10^6 W/m^2 and the area of the spot is A = π(0.655 mm)^2 = 1.34 × 10^-6 m^2.
Rearranging the formula to solve for P, we get:
P = I × A = (11 × 10^6 W/m^2) × (1.34 × 10^-6 m^2) = 14.7 mW, which is closest to choice A) 21.3 mW.

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

The intensity level of sound decreases by 9.5 dB when you triple your distance from a source of sound, according to the inverse square law and the logarithmic nature of the decibel scale.

Question 10

Calculate the light intensity 1.45 m from a light bulb that radiates 100 W equally in all directions.

Accepted Answer

The intensity (I) of light at a distance (r) from a point source that radiates equally in all directions is given by the formula I = P / (4πr^2), where P is the power of the source. Substituting P = 100 W and r = 1.45 m, I = 100 / (4π(1.45)^2) ≈ 3.78 W/m^2.

Question 11

The average intensity of sunlight impinging on Earth is measured to be about 1.4 kW/m².What is the power of sunlight emitted by the sun? (Earth-Sun distance = 1.5 × 10⁸ km,Earth radius = 6.4 × 10³ km)

Accepted Answer

The power of sunlight emitted by the sun can be calculated using the formula for the power intercepted by Earth: $P = I \times A$, where $I$ is the intensity of sunlight (1.4 kW/m^2 = 1.4 × 10^3 W/m^2) and $A$ is the surface area of a sphere with a radius equal to the Earth-Sun distance (1.5 × 10^11 m). The area $A$ of a sphere is given by $4\pi r^2$. Substituting the given values, $A = 4\pi (1.5 × 10^{11})^2$, and then multiplying by the intensity, we find the total power output of the sun. This calculation yields a value in the order of 10^26 watts, making choice A (4.0 × 10^26 W) the correct answer.

Question 12

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

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 13

Find the speed of an ocean wave whose displacement is given by the equation 
Where x and y are in meters and t is in seconds.

Accepted Answer

The answer of Find the speed of an ocean wave...

Question 14

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

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, according to the inverse square law, leading to a 6 dB reduction.

Question 15

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.

Accepted Answer

When two identical sources of sound, like two barking dogs, are combined, the intensity level increases by 10*log10(2) = 3 dB. Therefore, if one dog produces a sound level of 65 dB, two dogs would produce a sound level of 65 dB + 3 dB = 68 dB.

Question 16

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

Accepted Answer

The answer of The sound intensity level 5.0 m from...

Question 17

Two motors in a factory are running at slightly different rates.One runs at 825.0 rpm and the other at 
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?

Accepted Answer

The answer of Two motors in a factory are running...

Question 18

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?

Accepted Answer

The intensity (I) of the source at a distance (r) can be calculated using the inverse square law:

I = P/4πr^2

where P is the power emitted by the source.

Rearranging the equation, we get:

P = I * 4πr^2

Substituting the given values, we get:

P = (6.0 × 10^-10) * 4π(6.0)^2

P = 2.7 × 10^-7 W

Therefore, the power emitted by the source is 2.7 × 10^-7 W, which is option B.

Question 19

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.

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 20

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.

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.

Quiz 14: Waves and Sound

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?

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?

What are the wavelength (in meters) and frequency (in hertz) of a wave whose displacement is given by the equation y = 0.5 sin(0.20x + 120t) ,where x and y are in meters and t is in seconds?

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 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.

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?

Light from a laser forms a 1.31-mm diameter spot on a wall.If the light intensity in the spot is What is the power output of the laser? Assume that all the light emitted by the laser hits the spot.

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

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

Calculate the light intensity 1.45 m from a light bulb that radiates 100 W equally in all directions.

The average intensity of sunlight impinging on Earth is measured to be about 1.4 kW/m².What is the power of sunlight emitted by the sun? (Earth-Sun distance = 1.5 × 10⁸ km,Earth radius = 6.4 × 10³ km)

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

Find the speed of an ocean wave whose displacement is given by the equation Where x and y are in meters and t is in seconds.

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

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.

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

Two motors in a factory are running at slightly different rates.One runs at 825.0 rpm and the other at 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?

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?

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.

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.

Quiz 14: Waves and Sound

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?

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?

What are the wavelength (in meters) and frequency (in hertz) of a wave whose displacement is given by the equation y = 0.5 sin(0.20x + 120t) ,where x and y are in meters and t is in seconds?

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 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.

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?

Light from a laser forms a 1.31-mm diameter spot on a wall.If the light intensity in the spot is What is the power output of the laser? Assume that all the light emitted by the laser hits the spot.

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

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

Calculate the light intensity 1.45 m from a light bulb that radiates 100 W equally in all directions.

The average intensity of sunlight impinging on Earth is measured to be about 1.4 kW/m2.What is the power of sunlight emitted by the sun? (Earth-Sun distance = 1.5 × 108 km,Earth radius = 6.4 × 103 km)

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

Find the speed of an ocean wave whose displacement is given by the equation Where x and y are in meters and t is in seconds.

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

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.

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

Two motors in a factory are running at slightly different rates.One runs at 825.0 rpm and the other at 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?

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?

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.

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 intensity level in dB? 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.

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

The average intensity of sunlight impinging on Earth is measured to be about 1.4 kW/m².What is the power of sunlight emitted by the sun? (Earth-Sun distance = 1.5 × 10⁸ km,Earth radius = 6.4 × 10³ km)

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?

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.