Question 1

The vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m^-1)x - (7.22 s^-1)t]. What are the (a) speed and (b) amplitude of this wave?

Accepted Answer

The answer of The vertical displacement y(x,t) of a horizontal...

Question 2

What is the wave speed in a brass wire with a radius of 0.500 mm stretched with a tension of 125 N? The density of brass is 8.60 × 10³ kg/m³.

Accepted Answer

The wave speed in a stretched wire is given by the equation v = sqrt(T/μ), where T is the tension and μ is the mass per unit length (density times cross-sectional area). We have the values of T and ρ, so we just need to calculate the cross-sectional area using the radius: A = πr^2. Plugging in the values, we get:

v = sqrt(125 N / (8.60 x 10^3 kg/m^3 x π x (0.500 x 10^-3 m)^2))
v = 136 m/s

Therefore, the best choice is C, with a wave speed of 136 m/s.

Question 3

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 at a distance of 6 m from the source is given as 6.0 × 10^-10 W/m^2. 
The intensity at a distance r from a source that is radiating equally in all directions is given as: 
I = P/4πr^2
where P is the power emitted by the source.

Substituting the given values, we get:

6.0 × 10^-10 = P/4π(6.0)^2

Solving for P, we get: 
P = 2.7 × 10^-7 W

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

Question 4

Find the speed of an ocean wave whose displacement is given by the equation $y = 3.7 \cos ( 2.2 x - 5.6 t )$ where x and y are in meters and t is in seconds.

Accepted Answer

The speed of an ocean wave is given by the formula:$$v = \frac{\omega}{k}$$where $\omega$ is the angular frequency and $k$ is the wavenumber. The angular frequency is given by:$$\omega = 2\pi f$$where $f$ is the frequency. The wavenumber is given by:$$k = \frac{2\pi}{\lambda}$$where $\lambda$ is the wavelength. The wavelength is the distance between two consecutive crests or troughs of the wave. In this case, the wavelength is given by:$$\lambda = \frac{2\pi}{2.2} = 2.86 	ext{ m}$$The frequency is given by:$$f = \frac{5.6}{2\pi} = 0.89 	ext{ Hz}$$Therefore, the angular frequency is:$$\omega = 2\pi f = 2\pi (0.89) = 5.58 	ext{ rad/s}$$And the wavenumber is:$$k = \frac{2\pi}{\lambda} = \frac{2\pi}{2.86} = 2.19 	ext{ rad/m}$$Therefore, the speed of the wave is:$$v = \frac{\omega}{k} = \frac{5.58}{2.19} = 2.55 	ext{ m/s}$$Therefore, the correct answer is A.

Question 5

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 6

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 7

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

Let's call the distance to the explosion "d". We know that the time it takes for the vibrations to travel through the ground is equal to the time it takes for the sound to travel through the air. We can write this as:

d / 6.0 km/s = (d / 343 m/s) + 60 s

Simplifying this equation, we can start by converting the speed of sound through the ground to m/s:

6.0 km/s = 6000 m/s

Substituting this and multiplying both sides by 343 m/s, we get:

343d = 6000d + 2058000

Solving for d, we get:

d = 22 km

So the explosion was 22 km away from you. The best choice is therefore B.

Question 8

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

Accepted Answer

The ratio of intensities is given by:
ratio = 10^((I2 - I1)/10)
where I1 and I2 are the intensity levels in dB.
Plugging in the values given in the question, we get:
ratio = 10^((40 - 70)/10) = 10^(-3) = 1/1000
Therefore, the ratio of intensities is 1:1000, which is equivalent to 1000:1. Thus, the best choice is C, 1000:1.

Question 9

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 equation for the wave can be written as:
y(x,t) = 0.5sin(0.20x + 120t)

Comparing with the standard equation for a sinusoidal wave:
y(x,t) = Asin(kx - ωt + φ)
where,
A = amplitude = 0.5 m
k = wave number = 0.20 m⁻¹
ω = angular frequency = 120 rad/s (since ωt = 120t)
φ = phase constant

The wavelength λ and frequency f of the wave can be calculated as:
λ = 2π/k = 2π/0.20 = 31.4 m
f = ω/2π = 120/2π = 19.1 Hz

Hence, the wavelength and frequency of the wave are 31 m and 19 Hz respectively. Therefore, the correct choice is D.

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 vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m^-1)x - (7.22 s^-1)t]. What are the (a) wavelength and (b) period of this wave?

Accepted Answer

The answer of The vertical displacement y(x,t) of a horizontal...

Question 12

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 13

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 14

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 time it takes for the sound to reach our ears is equal to the time it takes for the stone to fall to the bottom of the well. We can use the formula for free fall to find this time:

d = 1/2 gt^2

where d is the distance (9.5 m) and g is the acceleration due to gravity (9.81 m/s^2). Solving for t, we get:

t = sqrt(2d/g) = sqrt(2*9.5/9.81) = 1.4 s

Therefore, the best choice is C.

Question 15

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 16

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 17

Light from a laser forms a 1.31-mm diameter spot on a wall. If the light intensity in the spot is $1.58 \times 10^4 \mathrm {~W} / \mathrm { m } ^ { 2 }$ what is the power output of the laser? Assume that all the light emitted by the laser hits the spot.

Accepted Answer

The power output of the laser is equal to the intensity of the light in the spot multiplied by the area of the spot. The area of the spot is given by:$$A = \pi r^2 = \pi (0.655 	imes 10^{-3} \mathrm{~m})^2 = 1.34 	imes 10^{-6} \mathrm{~m}^2$$Therefore, the power output of the laser is:$$P = IA = (1.58 	imes 10^4 \mathrm{~W/m^2})(1.34 	imes 10^{-6} \mathrm{~m}^2) = 21.3 \mathrm{~mW}$$

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 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 19

Two motors in a factory are running at slightly different rates. One runs at 825.0 rpm and the other at 786.0 ${ rpm } .$ 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 beat frequency is the difference in frequencies of the two motors: $ \frac{825.0 - 786.0}{60} = 0.65 $ Hz. The time between successive intensity increases is the inverse of the beat frequency: $ \frac{1}{0.65} \approx 1.54 $ s.

Question 20

A wire that is 1.0 m long with a mass of 90 g is under a tension of 710 N. When a transverse wave travels on the wire, its wavelength is 0.10 m and its amplitude is 6.5 mm. What is the frequency of this wave?

Accepted Answer

The answer of A wire that is 1.0 m long...

Quiz 15: Traveling Waves and Sound

The vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m^-1)x - (7.22 s^-1)t]. What are the (a) speed and (b) amplitude of this wave?

What is the wave speed in a brass wire with a radius of 0.500 mm stretched with a tension of 125 N? The density of brass is 8.60 × 10³ kg/m³.

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?

Find the speed of an ocean wave whose displacement is given by the equation $y = 3.7 \cos ( 2.2 x - 5.6 t )$ where x and y are in meters and t is in seconds.

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 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?

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

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?

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

The vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m^-1)x - (7.22 s^-1)t]. What are the (a) wavelength and (b) period of this wave?

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?

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?

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

Light from a laser forms a 1.31-mm diameter spot on a wall. If the light intensity in the spot is $1.58 \times 10^4 \mathrm {~W} / \mathrm { m } ^ { 2 }$ what is the power output of the laser? Assume that all the light emitted by the laser hits the spot.

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 wire that is 1.0 m long with a mass of 90 g is under a tension of 710 N. When a transverse wave travels on the wire, its wavelength is 0.10 m and its amplitude is 6.5 mm. What is the frequency of this wave?

Quiz 15: Traveling Waves and Sound

The vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 s-1)t]. What are the (a) speed and (b) amplitude of this wave?

What is the wave speed in a brass wire with a radius of 0.500 mm stretched with a tension of 125 N? The density of brass is 8.60 × 103 kg/m3.

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?

Find the speed of an ocean wave whose displacement is given by the equation y=3.7cos⁡(2.2x−5.6t) y = 3.7 \cos ( 2.2 x - 5.6 t ) y=3.7cos(2.2x−5.6t) where x and y are in meters and t is in seconds.

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 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?

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

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?

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

The vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 s-1)t]. What are the (a) wavelength and (b) period of this wave?

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?

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?

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

Light from a laser forms a 1.31-mm diameter spot on a wall. If the light intensity in the spot is 1.58×104 W/m21.58 \times 10^4 \mathrm {~W} / \mathrm { m } ^ { 2 }1.58×104 W/m2 what is the power output of the laser? Assume that all the light emitted by the laser hits the spot.

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 wire that is 1.0 m long with a mass of 90 g is under a tension of 710 N. When a transverse wave travels on the wire, its wavelength is 0.10 m and its amplitude is 6.5 mm. What is the frequency of this wave?

The vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m^-1)x - (7.22 s^-1)t]. What are the (a) speed and (b) amplitude of this wave?

What is the wave speed in a brass wire with a radius of 0.500 mm stretched with a tension of 125 N? The density of brass is 8.60 × 10³ kg/m³.

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?

Find the speed of an ocean wave whose displacement is given by the equation $y = 3.7 \cos ( 2.2 x - 5.6 t )$ where x and y are in meters and t is in seconds.

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 vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m^-1)x - (7.22 s^-1)t]. What are the (a) wavelength and (b) period of this wave?

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

Light from a laser forms a 1.31-mm diameter spot on a wall. If the light intensity in the spot is $1.58 \times 10^4 \mathrm {~W} / \mathrm { m } ^ { 2 }$ what is the power output of the laser? Assume that all the light emitted by the laser hits the spot.

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.