Question 1

Workmen are digging up the road using pneumatic tools.If a single tool creates a noise level of 88 decibels a few meters away,calculate the noise level if four such tools were in operation the same distance away.

Accepted Answer

Each additional tool increases the noise level by 3 decibels due to the logarithmic nature of the decibel scale. Therefore, four tools would create a level of 88 + (3*3) = 97 decibels, which rounds to 94 decibels. Option D is the closest to this value. Options A, C, and E are all far too high for the situation described.

Question 2

If you were to reduce the frequency of a wave on a string by a factor of 2 while keeping the speed and amplitude of the wave constant,the rate at which energy is delivered by the wave would

Accepted Answer

The energy of a wave is proportional to the square of the frequency. Therefore, reducing the frequency by a factor of 2 would reduce the energy by a factor of 4 (2^2). This means that the rate at which energy is delivered by the wave would also be reduced by a factor of 4, or to 25% of its previous value. Therefore, the correct answer is D.

Question 3

You have a rope that is 10 m long and has a mass of 0.2 kg.In addition,you have an oscillator that can generate a 5 Hz wave with an amplitude of 10 cm.What should the tension in the rope be if you need to transmit 10 W of power along the rope?

Accepted Answer

The answer of You have a rope that is 10...

Question 4

The intensity of a certain spherical wave is 8.0 W/m² at a distance of 1.0 m from the source.If the medium is isotropic and nonabsorbing,the intensity 100 m from the source is

Accepted Answer

The intensity of a spherical wave varies inversely with the square of the distance from the source. Therefore, at a distance of 100 m from the source, the intensity will be:

I = 8.0 W/m^2 * (1 m / 100 m)^2 = 8.0 * 10^-4 W/m^2

We can convert this to scientific notation as 8.0 * 10^-4 W/m^2 = 8.0 * 10^10 * 10^-14 W/m^2 = 8.0 * 10^10 nW/m^2.

Using the same unit conversion as in the question, we get:

8.0 * 10^10 nW/m^2 = 8.0 * 10^10 * 10^-9 W/m^2 = 8.0 * 10^1 W/m^2

Therefore, the answer is choice D, 8.0 × 10^1 W/m^2.

Question 5

If you were to quadruple the speed of a wave on a string while keeping the frequency and amplitude of the wave constant,the rate at which energy is delivered by the wave would

Accepted Answer

The energy of a wave is proportional to the square of its amplitude and the square of its frequency, but not directly proportional to its speed. Therefore, if the frequency and amplitude are constant but the speed is quadrupled, the energy delivered by the wave will be quadrupled as well.

Question 6

If you were to double the speed of a wave on a string while keeping the frequency and amplitude of the wave constant,the rate at which energy is delivered by the wave would

Accepted Answer

The answer of If you were to double the speed...

Question 7

The sound level of a dog's bark is 50 dB.The intensity of a rock concert is 10,000 times that of the dog's bark.What is the sound level of the rock concert?

Accepted Answer

The sound level in decibels (dB) can be calculated using the formula: $L = 10 \log_{10} \left(\frac{I}{I_0}\right)$, where $L$ is the sound level in dB, $I$ is the intensity of the sound, and $I_0$ is the reference intensity. A tenfold increase in intensity (10 times) results in an increase of 10 dB. Since the rock concert is 10,000 times the intensity of the dog's bark, this corresponds to a 40 dB increase (because $10 \log_{10}(10,000) = 40$). Adding this to the original 50 dB of the dog's bark gives us 90 dB.

Question 8

A noisy workplace has a noise level of 90 dB.You want to reduce this to a more comfortable 75 dB.By what factor must the power of the noise source be reduced? (That is,what is the ratio of the new power to the old?)

Accepted Answer

The sound level in decibels is calculated using the formula $L = 10 \log_{10}(\frac{P_1}{P_0})$, where $L$ is the sound level in decibels, $P_1$ is the power of the sound, and $P_0$ is a reference power. To find the factor by which the power must be reduced, we use the difference in decibels: $75 dB - 90 dB = -15 dB$. The equation becomes $-15 = 10 \log_{10}(\frac{P_{new}}{P_{old}})$. Solving for $\frac{P_{new}}{P_{old}}$ gives us a factor of approximately 0.032, meaning the power must be reduced by this factor to achieve the desired decrease in noise level.

Question 9

If you were to double the frequency of a wave on a string while keeping the speed and amplitude of the wave constant,the energy delivered by the wave would

Accepted Answer

The energy of a wave is proportional to the square of its frequency. Therefore, if the frequency is doubled, the energy delivered by the wave would quadruple.

Question 10

A wave of frequency f is transmitted on a string with tension T.If the tension is increased by a factor of 4 and the frequency and amplitude are unchanged,the power transmitted changed by

Accepted Answer

The power transmitted by a wave on a string is proportional to the square root of the tension. If the tension is increased by a factor of 4, the power increases by a factor of 2.

Question 11

A musical pitch is played at 60 dB.Another is played that sounds four times as loud.The sound intensity level of the second pitch is

Accepted Answer

The answer of A musical pitch is played at 60...

Question 12

The intensity of a wave at a certain point is I.A second wave has twice the energy density and three times the speed of the first.What is the intensity of the second wave?

Accepted Answer

Intensity is directly proportional to the square of the energy density and the square of the velocity. 
Let the energy density and speed of the first wave be E and v respectively. 
Given, the second wave has twice the energy density and three times the speed of the first wave. 
Energy density of the second wave = 2E and speed of the second wave = 3v.
So, 
Intensity of the first wave = E×v² 
Intensity of the second wave = 2E × (3v)² = 18E × v² 
Therefore, the ratio of the intensity of the second wave to the first wave is 
18E × v² / E×v² = 18 
Hence, the intensity of the second wave is 18 times the intensity of the first wave, i.e., 6I.

Question 13

Two sounds differ by 20 dB.This means that the louder sound is _____ times as intense and _____ times as loud.

Accepted Answer

The difference in intensity level between two sounds measured in decibels (dB) is calculated using the formula 10 * log(I1/I2), where I1 and I2 are the intensities of the two sounds. A difference of 20 dB means that the intensity ratio is 10^(20/10) = 100, so the louder sound is 100 times as intense. The perception of loudness, however, does not scale linearly with intensity; it's generally accepted that a 10 dB increase is perceived as roughly twice as loud. Therefore, a 20 dB increase would be perceived as four times as loud.

Question 14

At an outdoor bandstand,what would be the difference in the sound intensity level (dB)received by a listener 5 m from the bandstand and a listener 40 m from the bandstand,assuming there is no sound reflection? [$\beta$ = 10 log(I/I₀)]

Accepted Answer

The answer of At an outdoor bandstand,what would be the...

Question 15

Waves of amplitude 1.1 cm and wavelength 40 cm move along a 12-m long string that has a mass of 70 g and is under a tension of 15 N.Calculate the velocity of the wave.

Accepted Answer

The velocity of a wave on a string is given by the formula $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the string and $\mu$ is the mass per unit length of the string. Here, $T = 15\,N$ and the mass per unit length $\mu = \frac{70\,g}{12\,m} = \frac{70}{12 \times 1000}\,kg/m = \frac{7}{1200}\,kg/m$. Plugging these values into the formula gives $v = \sqrt{\frac{15}{7/1200}} = \sqrt{\frac{15 \times 1200}{7}} = \sqrt{2571.43}$ which is approximately $51\,m/s$.

Question 16

If you were to double the amplitude and halve the frequency of a wave on a string while keeping the amplitude of the wave constant,the rate at which energy is delivered by the wave would

Accepted Answer

Doubling the amplitude while halving the frequency, but keeping the amplitude constant, is contradictory. However, if we focus on the energy aspect, the energy transmitted by a wave is proportional to the square of its amplitude and is independent of its frequency. Therefore, if the amplitude is somehow kept constant despite the initial statement, the energy delivery rate by the wave would remain unchanged.

Question 17

The human ear can be sensitive to sound frequencies up to 20 kHz.What wavelength does this correspond to at normal temperature and pressure?

Accepted Answer

The speed of sound in air at normal temperature and pressure is approximately 343 m/s. The wavelength of a sound wave with a frequency of 20 kHz can be calculated using the formula: wavelength = speed of sound / frequency. 
Thus, wavelength = 343 m/s / 20,000 Hz = 0.01715 m = 17.15 mm. 
However, the question asks for the maximum sound frequency that the human ear can detect, which is 20 kHz. Therefore, the answer should be in the order of millimeters. The closest option is C, 16.5 mm.

Question 18

Waves of amplitude 1.3 cm move along a 14-m long string that has a mass of 90 g and is under a tension of 18 N.If the average total energy of the waves in the string is 5 J,calculate the frequency of the waves.

Accepted Answer

The velocity of the waves on the string can be found using the formula:

v = sqrt(T/μ)

where T is the tension, μ is the linear mass density (mass per unit length) of the string, and sqrt denotes the square root.

μ = m/L = 90 g / 14 m = 6.43 x 10^-3 kg/m

v = sqrt(18 N / 6.43 x 10^-3 kg/m) = 54.4 m/s

The energy of a wave on the string can be found using the formula:

E = 1/2 * (μ/L) * (Aω)^2

where A is the amplitude of the wave, ω is its frequency, and * denotes multiplication.

Solving for ω:

ω = sqrt(2E / (μAL^2))

ω = sqrt(2(5 J) / (6.43 x 10^-3 kg/m)(1.3 x 10^-2 m)(14 m)^2) = 129 Hz

Therefore, the frequency of the waves is 129 Hz.

Question 19

If a sound of intensity I = 1.0 F1F1F1S1F1F1F10 10^-6 W/m² falls on a detector of area A = 7.0 $\times$ 10^-5 m² (about the size of your eardrum),how much power is received by the detector?

Accepted Answer

The power received by the detector is calculated by multiplying the intensity of the sound by the area of the detector: $P = I \times A = 1.0 \times 10^{-6} \, \text{W/m}^2 \times 7.0 \times 10^{-5} \, \text{m}^2 = 7.0 \times 10^{-11} \, \text{W}$.

Question 20

Two sounds differ by 30 dB.The intensity of the louder sound I_L,compared with the softer I_S,is I_L/I_S.The value of the ratio is

Accepted Answer

The difference in decibels (dB) between two sounds is given by $10 \log_{10}(\frac{I_1}{I_2})$, where $I_1$ and $I_2$ are the intensities of the two sounds. Given a 30 dB difference, we have $30 = 10 \log_{10}(\frac{I_1}{I_2})$. Solving for $\frac{I_1}{I_2}$, we get $\frac{I_1}{I_2} = 10^{30/10} = 10^3 = 1000$.

Quiz 15: Wave Motion

Workmen are digging up the road using pneumatic tools.If a single tool creates a noise level of 88 decibels a few meters away,calculate the noise level if four such tools were in operation the same distance away.

If you were to reduce the frequency of a wave on a string by a factor of 2 while keeping the speed and amplitude of the wave constant,the rate at which energy is delivered by the wave would

You have a rope that is 10 m long and has a mass of 0.2 kg.In addition,you have an oscillator that can generate a 5 Hz wave with an amplitude of 10 cm.What should the tension in the rope be if you need to transmit 10 W of power along the rope?

The intensity of a certain spherical wave is 8.0 W/m² at a distance of 1.0 m from the source.If the medium is isotropic and nonabsorbing,the intensity 100 m from the source is

If you were to quadruple the speed of a wave on a string while keeping the frequency and amplitude of the wave constant,the rate at which energy is delivered by the wave would

If you were to double the speed of a wave on a string while keeping the frequency and amplitude of the wave constant,the rate at which energy is delivered by the wave would

The sound level of a dog's bark is 50 dB.The intensity of a rock concert is 10,000 times that of the dog's bark.What is the sound level of the rock concert?

A noisy workplace has a noise level of 90 dB.You want to reduce this to a more comfortable 75 dB.By what factor must the power of the noise source be reduced? (That is,what is the ratio of the new power to the old?)

If you were to double the frequency of a wave on a string while keeping the speed and amplitude of the wave constant,the energy delivered by the wave would

A wave of frequency f is transmitted on a string with tension T.If the tension is increased by a factor of 4 and the frequency and amplitude are unchanged,the power transmitted changed by

A musical pitch is played at 60 dB.Another is played that sounds four times as loud.The sound intensity level of the second pitch is

The intensity of a wave at a certain point is I.A second wave has twice the energy density and three times the speed of the first.What is the intensity of the second wave?

Two sounds differ by 20 dB.This means that the louder sound is _ times as intense and _ times as loud.

At an outdoor bandstand,what would be the difference in the sound intensity level (dB) received by a listener 5 m from the bandstand and a listener 40 m from the bandstand,assuming there is no sound reflection? [ $\beta$ = 10 log(I/I₀) ]

Waves of amplitude 1.1 cm and wavelength 40 cm move along a 12-m long string that has a mass of 70 g and is under a tension of 15 N.Calculate the velocity of the wave.

If you were to double the amplitude and halve the frequency of a wave on a string while keeping the amplitude of the wave constant,the rate at which energy is delivered by the wave would

The human ear can be sensitive to sound frequencies up to 20 kHz.What wavelength does this correspond to at normal temperature and pressure?

Waves of amplitude 1.3 cm move along a 14-m long string that has a mass of 90 g and is under a tension of 18 N.If the average total energy of the waves in the string is 5 J,calculate the frequency of the waves.

If a sound of intensity I = 1.0  10^-6 W/m² falls on a detector of area A = 7.0 $\times$ 10^-5 m² (about the size of your eardrum) ,how much power is received by the detector?

Two sounds differ by 30 dB.The intensity of the louder sound I_L,compared with the softer I_S,is I_L/I_S.The value of the ratio is

Quiz 15: Wave Motion

Workmen are digging up the road using pneumatic tools.If a single tool creates a noise level of 88 decibels a few meters away,calculate the noise level if four such tools were in operation the same distance away.

If you were to reduce the frequency of a wave on a string by a factor of 2 while keeping the speed and amplitude of the wave constant,the rate at which energy is delivered by the wave would

You have a rope that is 10 m long and has a mass of 0.2 kg.In addition,you have an oscillator that can generate a 5 Hz wave with an amplitude of 10 cm.What should the tension in the rope be if you need to transmit 10 W of power along the rope?

The intensity of a certain spherical wave is 8.0 W/m2 at a distance of 1.0 m from the source.If the medium is isotropic and nonabsorbing,the intensity 100 m from the source is

If you were to quadruple the speed of a wave on a string while keeping the frequency and amplitude of the wave constant,the rate at which energy is delivered by the wave would

If you were to double the speed of a wave on a string while keeping the frequency and amplitude of the wave constant,the rate at which energy is delivered by the wave would

The sound level of a dog's bark is 50 dB.The intensity of a rock concert is 10,000 times that of the dog's bark.What is the sound level of the rock concert?

A noisy workplace has a noise level of 90 dB.You want to reduce this to a more comfortable 75 dB.By what factor must the power of the noise source be reduced? (That is,what is the ratio of the new power to the old?)

If you were to double the frequency of a wave on a string while keeping the speed and amplitude of the wave constant,the energy delivered by the wave would

A wave of frequency f is transmitted on a string with tension T.If the tension is increased by a factor of 4 and the frequency and amplitude are unchanged,the power transmitted changed by

A musical pitch is played at 60 dB.Another is played that sounds four times as loud.The sound intensity level of the second pitch is

The intensity of a wave at a certain point is I.A second wave has twice the energy density and three times the speed of the first.What is the intensity of the second wave?

Two sounds differ by 20 dB.This means that the louder sound is _____ times as intense and _____ times as loud.

At an outdoor bandstand,what would be the difference in the sound intensity level (dB) received by a listener 5 m from the bandstand and a listener 40 m from the bandstand,assuming there is no sound reflection? [ β\betaβ = 10 log(I/I0) ]

Waves of amplitude 1.1 cm and wavelength 40 cm move along a 12-m long string that has a mass of 70 g and is under a tension of 15 N.Calculate the velocity of the wave.

If you were to double the amplitude and halve the frequency of a wave on a string while keeping the amplitude of the wave constant,the rate at which energy is delivered by the wave would

The human ear can be sensitive to sound frequencies up to 20 kHz.What wavelength does this correspond to at normal temperature and pressure?

Waves of amplitude 1.3 cm move along a 14-m long string that has a mass of 90 g and is under a tension of 18 N.If the average total energy of the waves in the string is 5 J,calculate the frequency of the waves.

If a sound of intensity I = 1.0  10-6 W/m2 falls on a detector of area A = 7.0 ×\times× 10-5 m2 (about the size of your eardrum) ,how much power is received by the detector?

Two sounds differ by 30 dB.The intensity of the louder sound IL,compared with the softer IS,is IL/IS.The value of the ratio is

The intensity of a certain spherical wave is 8.0 W/m² at a distance of 1.0 m from the source.If the medium is isotropic and nonabsorbing,the intensity 100 m from the source is

Two sounds differ by 20 dB.This means that the louder sound is _ times as intense and _ times as loud.

At an outdoor bandstand,what would be the difference in the sound intensity level (dB) received by a listener 5 m from the bandstand and a listener 40 m from the bandstand,assuming there is no sound reflection? [ $\beta$ = 10 log(I/I₀) ]

If a sound of intensity I = 1.0  10^-6 W/m² falls on a detector of area A = 7.0 $\times$ 10^-5 m² (about the size of your eardrum) ,how much power is received by the detector?

Two sounds differ by 30 dB.The intensity of the louder sound I_L,compared with the softer I_S,is I_L/I_S.The value of the ratio is