Question 1

Equal-wavelength waves of amplitude 0.27 m and 0.13 m interfere with one another.What is the resulting minimum amplitude that can result?

Accepted Answer

The answer of Equal-wavelength waves of amplitude 0.27 m and...

Question 2

A wave travels in a string at 58 m/s.A second string of 10% greater linear density has the same tension applied as in the first string.What will be the resulting wave speed in the second string?

Accepted Answer

The wave speed in a string is given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the string and $\mu$ is the linear density. If the second string has a 10% greater linear density, its linear density is 1.1 times that of the first string. Since the tension is the same in both strings, the wave speed in the second string will be $\frac{1}{\sqrt{1.1}}$ times the wave speed in the first string, which calculates to approximately 55 m/s.

Question 3

A wave on a string has a wavelength of 0.90 m at a frequency of 600 Hz.If a new wave at a frequency of 300 Hz is established in this same string under the same tension,what is the new wavelength?

Accepted Answer

The formula for the wavelength of a wave on a string is:
wavelength = (tension/linear density) x (1/frequency)^0.5
Since the tension and linear density of the string are the same for both waves, we can set the two wavelength equations equal to each other and solve for the new wavelength:
wavelength1 = wavelength2
(tension/linear density) x (1/frequency1)^0.5 = (tension/linear density) x (1/frequency2)^0.5
Simplifying and solving for wavelength2, we get:
wavelength2 = wavelength1 x (frequency1/frequency2)^0.5
Plugging in the values, we get:
wavelength2 = 0.90 m x (600 Hz/300 Hz)^0.5
wavelength2 = 0.90 m x 2^0.5
wavelength2 = 1.8 m
Therefore, the new wavelength is 1.8 m, which corresponds to choice B.

Question 4

If the speed of a wave on a violin string is 400 m/s,what will be the speed of the wave if the tension in the string is halved?

Accepted Answer

The speed of a wave on a string is proportional to the square root of the tension. If the tension is halved, the speed is reduced by a factor of √2, so the new speed is 400/√2 = 400/1.414 ≈ 280 m/s.

Question 5

The superposition principle has to do with which of the following?

Accepted Answer

The superposition principle states that when two or more waves interact, the displacement of the resulting wave at any point is equal to the sum of the displacements of the individual waves at that point. In other words, the waves add together. This principle is important in understanding a wide range of wave phenomena, from interference patterns to resonance in musical instruments.

Question 6

A string with mass per unit length 1 is under tension T₁.A wave traveling along this string has a speed v₁.A wave traveling along a second string has speed v₂.If v₂ = 4v₁,what could be the tension,T₂,and mass per unit length, 2,of the second string?

Accepted Answer

The answer of A string with mass per unit length...

Question 7

A steel piano string is attached,under tension,at each end to secure posts.When gently struck,a faint note can be detected coming from the string.The string is then cooled by blowing cold air over it and then is struck again.How does the note now detected compare to the previous one.

Accepted Answer

Cooling the steel piano string causes it to contract, increasing the tension in the string. This increased tension results in a higher frequency of vibration when the string is struck, producing a note of higher pitch.

Question 8

Consider two identical and symmetrical wave pulses on a string.Suppose the first pulse reaches the fixed end of the string and is reflected back and then meets the second pulse.When the two pulses overlap exactly,the superposition principle predicts that the amplitude of the resultant pulses,at that moment,will be what factor times the amplitude of one of the original pulses?

Accepted Answer

The answer of Consider two identical and symmetrical wave pulses...

Question 9

Wave #1 has frequency f₁ and wavelength λ₁.Wave #2 has frequency f₂ = 6 f₁ and wavelength λ₂ = 2λ₁.How does the speed v₂ of wave #2 compare with the speed v₁ of wave #1?

Accepted Answer

The speed of a wave is given by the product of its frequency and wavelength. Therefore, the speed of wave #2 is v₂ = f₂λ₂ = (6f₁)(2λ₁) = 12f₁λ₁. The speed of wave #1 is v₁ = f₁λ₁. Therefore, the ratio of the speeds is v₂/v₁ = (12f₁λ₁)/(f₁λ₁) = 12. Therefore, v₂ = 12v₁.

Question 10

If a wave pulse is reflected from a free boundary,which of the following choices best describes what happens to the reflected pulse?

Accepted Answer

When a wave pulse is reflected from a free boundary, it remains upright, meaning it does not invert. This is because a free boundary allows the end of the medium to move freely, reflecting the wave without flipping it over.

Question 11

Two water waves meet at the same point,one having a displacement above equilibrium of 50 cm and the other having a displacement above equilibrium of 90 cm.At this moment,what is the resulting displacement above equilibrium?

Accepted Answer

When two waves meet, their displacements add together due to the principle of superposition. Therefore, the resulting displacement is 50 cm + 90 cm = 140 cm.

Question 12

A string is strung horizontally with a fixed tension.A wave of frequency 60.0 Hz is sent along the string,and it has a wave speed of 58.4 m/s.Then a second wave,one of frequency 120 Hz,is sent along the string.What is the wave speed of the second wave?​

Accepted Answer

The wave speed on a string under a fixed tension does not depend on the frequency of the wave. Therefore, if the first wave travels at 58.4 m/s, the second wave, regardless of its frequency, will also travel at 58.4 m/s.

Question 13

A wave is traveling in a string at 50 m/s.When the tension is then increased 18%,what will be the resulting wave speed?​

Accepted Answer

The wave speed in a string is given by the equation v = √(T/μ), where T is the tension in the string and μ is the linear mass density. Since the string is the same, μ is constant. Therefore, if the tension is increased by 18%, the wave speed will increase by √(1.18) = 1.09 or 9%. 
So the resulting wave speed will be 50 x 1.09 = 54 m/s. Therefore, the correct choice is B.

Quiz 13: Vibrations and Waves