Question 1

A long string is pulled so that the tension in it increases by a factor of three.If the change in length is negligible,by what factor does the wave speed change?

Accepted Answer

The answer of A long string is pulled so that...

Question 2

Tripling both the tension in a guitar string and its mass per unit length will result in changing the wave speed in the string by what factor?

Accepted Answer

The wave speed on a string is given by the formula v = sqrt(T/μ), where T is the tension and μ is the mass per unit length. Tripling both T and μ results in v = sqrt(3T/3μ) = sqrt(T/μ), so the wave speed remains unchanged.

Question 3

A string is strung horizontally with a fixed tension.A wave of frequency 100 Hz is sent along the string,and it has a wave speed of 50.0 m/s.Then a second wave,one of frequency 200 Hz,is sent along the string.What is the wave speed of the second wave?

Accepted Answer

The wave speed is determined by the tension and the linear mass density of the string, which are both constants in this scenario. Therefore, the wave speed of the second wave is also 50.0 m/s. The frequency of the wave does not affect the wave speed.

Question 4

Transverse waves travel with a speed of 200 m/s along a taut copper wire that has a diameter of 1.50 mm.What is the tension in the wire? (The density of copper is 8.93 g/cm³. )

Accepted Answer

The answer of Transverse waves travel with a speed of...

Question 5

For a wave traveling in a string,by what factor would the tension need to be increased to double the wave speed?

Accepted Answer

The wave speed in a string is given by v = √(T/μ), where T is the tension in the string and μ is the linear density of the string. If the wave speed is doubled, then v' = 2v, and we can write:

2v = √(T'/μ)

where T' is the increased tension needed to achieve this speed. Solving for T', we get:

T' = 4T

Therefore, the tension must be increased by a factor of 4 to double the wave speed. The closest answer choice is C, 4.0.

Question 6

What is the phase difference when two waves,traveling in the same medium,undergo constructive interference?

Accepted Answer

Constructive interference occurs when two waves have the same frequency and amplitude and are in phase with each other. This means that the crests of the waves line up with each other, as well as the troughs. When this happens, the phase difference between the waves is 0 degrees. Therefore, choice D is the correct answer.

Question 7

Waves propagate at 8.0 m/s along a stretched string.The end of the string is vibrated up and down once every 1.5 s.What is the wavelength of the waves that travel along the string?

Accepted Answer

The answer of Waves propagate at 8.0 m/s along a...

Question 8

If a long spring with spring constant k is cut into 4 equal lengths,what is the spring constant of each of the 4 shorter springs?

Accepted Answer

When a spring is cut into shorter lengths, the spring constant of each shorter spring increases. For a spring cut into n equal parts, the spring constant of each part becomes n times the original spring constant. Therefore, if the spring is cut into 4 equal lengths, the spring constant of each shorter spring is 4k.

Question 9

An earthquake emits both P-waves and S-waves that travel at different speeds through the Earth.A P-wave travels at 8 000 m/s and an S-wave at 4 000 m/s.If P-waves are received at a seismic station 30.0 s before an S-wave arrives,how far is the station from the earthquake center?

Accepted Answer

The answer of An earthquake emits both P-waves and S-waves...

Question 10

A wave travels in a string at 60 m/s.A second string of 20% 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 the formula $ v = \sqrt{\frac{T}{\mu}} $, where $ T $ is the tension and $ \mu $ is the linear density. If the second string has 20% greater linear density, its linear density is $ 1.2\mu $. The wave speed in the second string will be $ v = \sqrt{\frac{T}{1.2\mu}} = \frac{1}{\sqrt{1.2}} \times 60 \approx 55 $ m/s.

Question 11

Two water waves meet at the same point,one having a displacement above equilibrium of 60 cm and the other having a displacement above equilibrium of 80 cm.At this moment,what is the resulting displacement above equilibrium?

Accepted Answer

When two waves meet, their displacements add together. Here, both displacements are above equilibrium, so they add up to 60 cm + 80 cm = 140 cm.

Question 12

A wave is traveling in a string at 60 m/s.When the tension is then increased 20%,what will be the resulting wave speed?

Accepted Answer

The wave speed in a string is given by the equation v = sqrt(T/μ), where T is the tension in the string and μ is the mass per unit length. 
If the tension is increased by 20%, then the new tension becomes T' = T + 0.2T = 1.2T. 
Therefore, the new wave speed becomes v' = sqrt((1.2T)/μ) = sqrt(1.2)*sqrt(T/μ) = 1.095*60 m/s = 65.7 m/s, which is closest to option B) 66 m/s.

Question 13

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 total displacement at any point is the sum of the individual displacements of each wave. This principle is fundamental to understanding wave behavior and is used in fields such as physics, engineering, and astronomy.

Question 14

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 15

A 2.0-m long piano string of mass 10 g is under a tension of 338 N.Find the speed with which a wave travels on this string.

Accepted Answer

The speed of a wave on a string is given by the formula $ v = \sqrt{\frac{T}{\mu}} $, where $ T $ is the tension and $ \mu $ is the linear mass density. The linear mass density $ \mu $ is the mass per unit length, which is $ \frac{10 \, \text{g}}{2.0 \, \text{m}} = 0.005 \, \text{kg/m} $. Substituting the values, $ v = \sqrt{\frac{338 \, \text{N}}{0.005 \, \text{kg/m}}} = 260 \, \text{m/s} $.

Question 16

When an object is moving in simple harmonic motion,which of the following is at a minimum when the displacement from equilibrium is zero?

Accepted Answer

When an object is at the equilibrium position, it is momentarily at rest and its displacement is zero. According to the equation of simple harmonic motion, acceleration is directly proportional to displacement and in the opposite direction. Therefore, when displacement is zero, acceleration is also zero. This makes B - the magnitude of the acceleration - at a minimum when displacement is zero.

Question 17

Tripling the mass per unit length of a guitar string will result in changing the wave speed in the string by what factor?

Accepted Answer

The answer of Tripling the mass per unit length of...

Question 18

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 waves in air is 330 m/s,what is the smallest size insect they can detect?

Accepted Answer

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

Question 19

Equal wavelength waves of amplitude 0.25 m and 0.15 m interfere with one another.What is the resulting minimum amplitude that can result?

Accepted Answer

The resulting minimum amplitude would occur when the waves are exactly out of phase, meaning the peak of one wave coincides with the trough of the other. In this case, the amplitudes would subtract, resulting in a minimum amplitude of 0.25 m - 0.15 m = 0.1 m. Choice B is the closest to this value.

Question 20

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...

Quiz 13: Vibrations and Waves