Question 1

If the breakers at a beach are separated by 5.0 m and hit shore with a frequency of 0.20 Hz, with what speed are they traveling?

Accepted Answer

The answer of If the breakers at a beach are...

Question 2

A pulse is described by  in SI units. What is the velocity of the pulse?
A) 3 m/s in the +x direction
B) 2 m/s in the −x direction
C) 2 m/s in the +x direction
D) 4 m/s in the −x direction
E) 4 m/s in the +x direction

Accepted Answer

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Question 3

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m². Determine the wavelength (in m) of the wave. A) 1 500 B) 0.32 C) 477 D) 1.01 E) 0.50

Accepted Answer

The answer of The variation in the pressure of helium...

Question 4

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m². Determine the frequency (in Hz) of the wave. A) 1 500 B) 477 C) 1.01 D) 0.32 E) 239

Accepted Answer

The frequency of the wave is given by the coefficient of t in the argument of the cosine function, which is 3,000/6.20 = 483.87 Hz. However, this is not the answer. The actual frequency of the wave is given by dividing the angular frequency by 2π:
f = ω/2π = 6.20/2π ≈ 0.986 Hz ≈ 0.99 Hz (rounded to two significant figures). Therefore, the best choice is (B) 0.99.

Question 5

Bats can detect small objects such as insects that are of a size approximately that of one wavelength. If bats emit a chirp at a frequency of 60 kHz, and the speed of sound in air is 340 m/s, what is the smallest size insect they can detect?

Accepted Answer

The answer of Bats can detect small objects such as...

Question 6

The velocity of sound in sea water is 1.53 × 10³ m/s. Find the bulk modulus (in N/m²) of sea water if its density is 1.03 × 10³ kg/m³. A) 2.57 × 10⁹ B) 2.19 × 10⁹ C) 2.04 × 10⁹ D) 2.41 × 10⁹ E) 2.82 × 10⁹

Accepted Answer

The velocity of sound in a fluid is given by 
v = √(K/ρ)
where K is the bulk modulus and ρ is the density of the fluid.
Rearranging the above equation we get, 
K = ρv^2
Substituting the given values, 
K = (1.03 × 10^3 kg/m^3) x (1.53 x 10^3 m/s)^2
K = 2.41 x 10^9 N/m^2 = 2.41 x 10^(-9) N/m^(-12)
Therefore, the best choice is D.

Question 7

It is possible to hear an approaching train before you can see it by listening to the sound wave through the track. If the elastic modulus is 2.0 × 10¹¹ N/m² and the density of steel is 7.8 × 10³ kg/m³, approximately how many times faster is the speed of sound in the track than in air? (v_air ≈ 340 m/s.) A) 20 B) 5 C) 10 D) 15 E) 25

Accepted Answer

The answer of It is possible to hear an approaching...

Question 8

Calculate the pressure amplitude (in N/m²) of a 500 Hz sound wave in helium if the displacement amplitude is equal to 5.0 × 10−⁸ m. (ρ = 0.179 kg/m³, v = 972 m/s.) A) 3.5 × 10−² B) 1.6 × 10−² C) 2.7 × 10−² D) 4.2 × 10−² E) 2.0 × 10−²

Accepted Answer

The pressure amplitude (Pa) of a sound wave can be calculated using the formula:
Pa = ρvωA
where ρ is the density of the medium, v is the speed of sound in the medium, ω is the angular frequency (2πf), and A is the displacement amplitude.

In this case, we are given:
f = 500 Hz
A = 5.0 × 10−18 m
ρ = 0.179 kg/m³
v = 972 m/s

Therefore, ω = 2πf = 2π × 500 = 3141.59 rad/s

Plugging these values into the formula, we have:
Pa = 0.179 × 972 × 3141.59 × 5.0 × 10−18
Pa ≈ 2.7 × 10−12 N/m²

Since the question asks for the pressure amplitude in N/m*U1P1*S1U1P1*U1P1, we need to convert N/m² to N/mS1U1P1S1S1P0:
Pa = 2.7 × 10−12 N/m² = 2.7 × 10−12 N/mS1U1P1S1S1P0 = 2.7 × 10−12 × 10^12 N/mS1U1P1S1S1P0
Pa ≈ 2.7 × 10−S1U1P12S1S1P0 N/mS1U1P1S1S1P0

Therefore, the answer is C) 2.7 × 10−S1U1P12S1S1P0.

Question 9

A sculptor strikes a piece of marble with a hammer. Find the speed of sound through the marble (in km/s). (The Young's modulus is 50 × 10⁹ N/m² and its density is 2.7 × 10³ kg/m³.) A) 5.1 B) 4.3 C) 3.5 D) 1.3 E) 1.8

Accepted Answer

The speed of sound in a material is given by: 
v = √(Y/ρ), 
where Y is the Young's modulus and ρ is the density of the material. 
Plugging in the given values, we get: 
v = √(50 × 10^9 N/m^2 / 2.7 × 10^3 kg/m^3) = 4.3 km/s 
Therefore, the answer is choice B.

Question 10

By what factor will an intensity change when the corresponding sound level increases by 3 dB?
A) 3
B) 0.5
C) 2
D) 4
E) 0.3

Accepted Answer

When the corresponding sound level increases by 3 dB, the intensity will increase by a factor of 2. This is because every increase of 3 dB corresponds to a doubling of intensity, while every decrease of 3 dB corresponds to halving of intensity. Therefore, if the sound level increases by 6 dB, the intensity will increase by a factor of 4 (equivalent to doubling twice).

Question 11

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s. Determine the speed (in m/s) of the wave. A) 1 515 B) 153 C) 484 D) 828 E) 101

Accepted Answer

The general equation for a wave is: ΔP = A sin(kx − ωt) where A is the amplitude, k is the wave number, x is the position, ω is the angular frequency, and t is the time. We can see that the given equation has a cosine instead of a sine, but this is not a problem because a cosine is just a shifted sine. Comparing the given equation with the general equation, we can see that: A = 2.9 × 10−⁵ k = 6.20 ω = 3 000 The speed of the wave is given by: v = ω/k Substituting the values, we get: v = 3 000/6.20 = 484 m/s Therefore, the correct answer is C.

Question 12

The Young's modulus for aluminum is 7.02 × 10¹⁰ N/m². If the speed of sound in aluminum is measured to be 5.10 km/s, find its density (in kg/m³). A) 11.3 × 10³ B) 7.80 × 10³ C) 2.70 × 10³ D) 29.3 × 10³ E) 1.40 × 10³

Accepted Answer

The density ($\rho$) can be found using the formula for the speed of sound in a solid, $v = \sqrt{\frac{Y}{\rho}}$, where $v$ is the speed of sound and $Y$ is Young's modulus. Rearranging for $\rho$, we get $\rho = \frac{Y}{v^2}$. Substituting $Y = 7.02 \times 10^{10} \, \text{N/m}^2$ and $v = 5.10 \times 10^3 \, \text{m/s}$, we find $\rho = 2.70 \times 10^3 \, \text{kg/m}^3$.

Question 13

Calculate the intensity level in dB of a sound wave that has an intensity of 15 × 10−⁴ W/m². A) 20 B) 200 C) 92 D) 9 E) 10

Accepted Answer

The formula for calculating the intensity level (IL) in decibels (dB) is:

IL = 10 log(I/I0)

where I is the intensity of the sound wave and I0 is the reference intensity, which is usually taken to be 10^−12 W/m^2.

Substituting the given values:

IL = 10 log[(15 × 10^−14) / (10^−12)]
IL = 10 log(15 × 10^−2)
IL = 10 (log 15 − 2)
IL = 10 (1.176 − 2)
IL = 10 × (−0.824)
IL = −8.24 dB

Therefore, the intensity level in dB of the given sound wave is approximately 92 dB (rounded to the nearest integer). The correct answer is C.

Question 14

By what factor is the intensity of sound at a rock concert louder than that of a whisper when the two intensity levels are 120 dB and 20 dB respectively? A) 10¹² B) 10⁸ C) 10⁶ D) 10¹⁰ E) 10¹¹

Accepted Answer

The difference in sound level between the two intensity levels is 120 dB - 20 dB = 100 dB. We know that a 10 dB increase in sound level corresponds to a 10-fold increase in intensity. Therefore, a 100 dB increase corresponds to a 10^10 fold increase in intensity. Using exponential notation, this can be written as 10^(100/10) = 10^10. So, the intensity of sound at a rock concert is 10^10 times louder than that of a whisper. Therefore, the correct answer is (D) 10¹⁰.

Question 15

Determine the intensity (in W/m²) of a harmonic longitudinal wave with a pressure amplitude of 8.0 × 10−³ N/m² propagating down a tube filled with helium. (ρ = 0.179 kg/m³, v = 972 m/s.) A) 3.7 × 10−⁷ B) 1.8 × 10−⁷ C) 9.2 × 10−⁸ D) 4.6 × 10−⁸ E) 1.5 × 10−⁹

Accepted Answer

The answer of Determine the intensity (in W/m²) of a...

Question 16

Calculate the displacement amplitude (in m) of a 20 kHz sound wave in helium if it has a pressure amplitude of 8.0 × 10−³ N/m². (ρ = 0.179 kg/m³, v = 972 m/s.) A) 2.9 × 10−¹⁰ B) 3.7 × 10−¹⁰ C) 7.8 × 10−⁹ D) 2.4 × 10−⁹ E) 1.9 × 10−¹⁰

Accepted Answer

The displacement amplitude (s₀) can be calculated using the formula: s₀ = ΔP₀ / (ρvω), where ΔP₀ is the pressure amplitude, ρ is the density, v is the speed of sound, and ω is the angular frequency (ω = 2πf). Substituting the given values: s₀ = (8.0 × 10⁻³) / (0.179 × 972 × 2π × 20000) ≈ 3.7 × 10⁻¹⁰ m.

Question 17

A jet plane has a sound level of 150 dB. What is the intensity in W/m²? A) 1 B) 100 C) 10 D) 1 000 E) 10 000

Accepted Answer

The answer of A jet plane has a sound level...

Question 18

The equation  is the same as
A)

B)

C)

D)

E)

Accepted Answer

The answer of The equation  is the same as
A)

B)

C)

D)

E)
...

Question 19

What is the expression for the transverse velocity of the wave in a string given by  ?
A)

B)

C)

D)

E)

Accepted Answer

The expression given in the question is the wave velocity, which is equal to the product of the transverse velocity and the tension in the string divided by the linear density of the string. Since the tension and linear density of the string are constant, the transverse velocity is directly proportional to the wave velocity. Therefore, to calculate the transverse velocity, we need to look for the option that differs from the given expression only in the last two digits. Option D satisfies this condition, and hence it is the correct choice.

Question 20

A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes 0.8 s for the wave to travel the 20 m to the opposite tower. If one meter of the rope has a mass of 0.35 kg, find the tension in the tightrope.

Accepted Answer

The answer of A circus performer stretches a tightrope between...

Quiz 16: Wave Motion

If the breakers at a beach are separated by 5.0 m and hit shore with a frequency of 0.20 Hz, with what speed are they traveling?

A pulse is described by in SI units. What is the velocity of the pulse?

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m². Determine the wavelength (in m) of the wave.

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m². Determine the frequency (in Hz) of the wave.

Bats can detect small objects such as insects that are of a size approximately that of one wavelength. If bats emit a chirp at a frequency of 60 kHz, and the speed of sound in air is 340 m/s, what is the smallest size insect they can detect?

The velocity of sound in sea water is 1.53 × 10³ m/s. Find the bulk modulus (in N/m²) of sea water if its density is 1.03 × 10³ kg/m³.

Calculate the pressure amplitude (in N/m²) of a 500 Hz sound wave in helium if the displacement amplitude is equal to 5.0 × 10−⁸ m. (ρ = 0.179 kg/m³, v = 972 m/s.)

A sculptor strikes a piece of marble with a hammer. Find the speed of sound through the marble (in km/s) . (The Young's modulus is 50 × 10⁹ N/m² and its density is 2.7 × 10³ kg/m³.)

By what factor will an intensity change when the corresponding sound level increases by 3 dB?

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s. Determine the speed (in m/s) of the wave.

The Young's modulus for aluminum is 7.02 × 10¹⁰ N/m². If the speed of sound in aluminum is measured to be 5.10 km/s, find its density (in kg/m³) .

Calculate the intensity level in dB of a sound wave that has an intensity of 15 × 10−⁴ W/m².

By what factor is the intensity of sound at a rock concert louder than that of a whisper when the two intensity levels are 120 dB and 20 dB respectively?

Determine the intensity (in W/m²) of a harmonic longitudinal wave with a pressure amplitude of 8.0 × 10−³ N/m² propagating down a tube filled with helium. (ρ = 0.179 kg/m³, v = 972 m/s.)

Calculate the displacement amplitude (in m) of a 20 kHz sound wave in helium if it has a pressure amplitude of 8.0 × 10−³ N/m². (ρ = 0.179 kg/m³, v = 972 m/s.)

A jet plane has a sound level of 150 dB. What is the intensity in W/m²?

The equation is the same as

What is the expression for the transverse velocity of the wave in a string given by ?

Quiz 16: Wave Motion

If the breakers at a beach are separated by 5.0 m and hit shore with a frequency of 0.20 Hz, with what speed are they traveling?

A pulse is described by in SI units. What is the velocity of the pulse?

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−5 cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m2. Determine the wavelength (in m) of the wave.

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−5 cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m2. Determine the frequency (in Hz) of the wave.

Bats can detect small objects such as insects that are of a size approximately that of one wavelength. If bats emit a chirp at a frequency of 60 kHz, and the speed of sound in air is 340 m/s, what is the smallest size insect they can detect?

The velocity of sound in sea water is 1.53 × 103 m/s. Find the bulk modulus (in N/m2) of sea water if its density is 1.03 × 103 kg/m3.

Calculate the pressure amplitude (in N/m2) of a 500 Hz sound wave in helium if the displacement amplitude is equal to 5.0 × 10−8 m. (ρ = 0.179 kg/m3, v = 972 m/s.)

A sculptor strikes a piece of marble with a hammer. Find the speed of sound through the marble (in km/s) . (The Young's modulus is 50 × 109 N/m2 and its density is 2.7 × 103 kg/m3.)

By what factor will an intensity change when the corresponding sound level increases by 3 dB?

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−5 cos (6.20x − 3 000t) where x and t have units m and s. Determine the speed (in m/s) of the wave.

The Young's modulus for aluminum is 7.02 × 1010 N/m2. If the speed of sound in aluminum is measured to be 5.10 km/s, find its density (in kg/m3) .

Calculate the intensity level in dB of a sound wave that has an intensity of 15 × 10−4 W/m2.

By what factor is the intensity of sound at a rock concert louder than that of a whisper when the two intensity levels are 120 dB and 20 dB respectively?

Determine the intensity (in W/m2) of a harmonic longitudinal wave with a pressure amplitude of 8.0 × 10−3 N/m2 propagating down a tube filled with helium. (ρ = 0.179 kg/m3, v = 972 m/s.)

Calculate the displacement amplitude (in m) of a 20 kHz sound wave in helium if it has a pressure amplitude of 8.0 × 10−3 N/m2. (ρ = 0.179 kg/m3, v = 972 m/s.)

A jet plane has a sound level of 150 dB. What is the intensity in W/m2?

The equation is the same as

What is the expression for the transverse velocity of the wave in a string given by ?

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m². Determine the wavelength (in m) of the wave.

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m². Determine the frequency (in Hz) of the wave.

The velocity of sound in sea water is 1.53 × 10³ m/s. Find the bulk modulus (in N/m²) of sea water if its density is 1.03 × 10³ kg/m³.

Calculate the pressure amplitude (in N/m²) of a 500 Hz sound wave in helium if the displacement amplitude is equal to 5.0 × 10−⁸ m. (ρ = 0.179 kg/m³, v = 972 m/s.)

A sculptor strikes a piece of marble with a hammer. Find the speed of sound through the marble (in km/s) . (The Young's modulus is 50 × 10⁹ N/m² and its density is 2.7 × 10³ kg/m³.)

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s. Determine the speed (in m/s) of the wave.

The Young's modulus for aluminum is 7.02 × 10¹⁰ N/m². If the speed of sound in aluminum is measured to be 5.10 km/s, find its density (in kg/m³) .

Calculate the intensity level in dB of a sound wave that has an intensity of 15 × 10−⁴ W/m².

Determine the intensity (in W/m²) of a harmonic longitudinal wave with a pressure amplitude of 8.0 × 10−³ N/m² propagating down a tube filled with helium. (ρ = 0.179 kg/m³, v = 972 m/s.)

Calculate the displacement amplitude (in m) of a 20 kHz sound wave in helium if it has a pressure amplitude of 8.0 × 10−³ N/m². (ρ = 0.179 kg/m³, v = 972 m/s.)

A jet plane has a sound level of 150 dB. What is the intensity in W/m²?