Question 1

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?
A)also 60 m/s
B)66 m/s
C)72 m/s
D)55 m/s

Accepted Answer

The wave speed is dependent on the tension and the mass per unit length of the string. According to the question, the tension in the string is increased by 20%, which means that the wave speed will also increase because the tension is directly proportional to the wave speed.

The relationship between wave speed, tension, and mass per unit length is given by the equation:

v = sqrt(T/μ)

Where v is wave speed, T is tension, and μ is mass per unit length.

Since the mass per unit length of the string is not given and does not change in the question, we can assume it to be constant.

Therefore, the wave speed after the tension is increased by 20% can be calculated using the following equation:

v' = sqrt(1.2T/μ)

Where v' is the new wave speed.

Substituting the given values, we get:

v' = sqrt(1.2 * 60 / μ)

We can see that μ is an unknown constant, so we cannot calculate the exact wave speed. However, we can compare the values of v and v' to determine which answer choice is correct.

Since the square root of 1.2 is approximately 1.095 and the mass per unit length is constant, we can say that the new wave speed is approximately 1.095 times the original wave speed.

Therefore, the new wave speed is:

v' = 1.095 * 60 = 65.7 m/s

Rounding off to the nearest whole number, the answer is B) 66 m/s.

Question 2

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?
A)0.15 m
B)0.10 m
C)0 m
D)-0.40 m

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 3

When an object is moving in simple harmonic motion, which of the following is at a minimum when the displacement from equilibrium is zero?
A)the magnitude of the velocity
B)the magnitude of the acceleration
C)the kinetic energy
D)the total mechanical energy

Accepted Answer

When the displacement from equilibrium is zero, the object is at its maximum displacement and changing direction. Therefore, the velocity is at its maximum and the acceleration is at its minimum, which corresponds to the point of the object reaching equilibrium. The kinetic energy and total mechanical energy are not necessarily at a minimum when the displacement is zero.

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.) A)1 890 N B)1 260 N C)631 N D)315 N

Accepted Answer

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

Question 5

Two identical springs, each with spring constant k, are attached in parallel to a mass, which is then set into simple harmonic motion.What would be the spring constant of a single spring which would result in the same frequency of oscillation as the parallel springs?
A)k
B)2k
C)k/2
D)

Accepted Answer

The answer of Two identical springs, each with spring constant...

Question 6

What is the phase difference when two waves, traveling in the same medium, undergo constructive interference?
A)270$\degree$
B)180$\degree$
C)90$\degree$
D)0$\degree$

Accepted Answer

Constructive interference occurs when two waves are in phase with each other, meaning their crests and troughs align perfectly. The phase difference between them is therefore 0 degrees.

Question 7

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?
A)also 60 m/s
B)66 m/s
C)72 m/s
D)55 m/s

Accepted Answer

The answer of A wave travels in a string at...

Question 8

A pendulum on the Earth has a period T.The acceleration of due to gravity on Mars is less than that on the Earth, and the acceleration due to gravity on the Moon is even less.Where would the period of an identical pendulum be the least?
A)on the Earth
B)on the Moon
C)on Mars
D)The period of a pendulum would be the same on the Earth, Moon, and Mars since the period depends on the pendulum's length which is the same for identical pendula.

Accepted Answer

The period of a pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity. Since $g$ is highest on Earth compared to Mars and the Moon, the period $T$ is least on Earth.

Question 9

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.
A)130 m/s
B)260 m/s
C)520 m/s
D)1 040 m/s

Accepted Answer

The answer of A 2.0-m long piano string of mass...

Question 10

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?
A)It is still k.
B)It is k/4.
C)It is 4 k.
D)It is k/16.

Accepted Answer

The answer of If a long spring with spring constant...

Question 11

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?
A)3.0
B)1.7
C)0.58
D)0.33

Accepted Answer

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

Question 12

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?
A)0.58
B)1.00 (i.e., no change)
C)1.73
D)3.00

Accepted Answer

The answer of Tripling both the tension in a guitar...

Question 13

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?
A)25.0 m/s
B)50.0 m/s
C)70.7 m/s
D)100 m/s

Accepted Answer

The wave speed of a string depends on the tension and the linear mass density of the string, not on the frequency of the wave. Therefore, the wave speed of the second wave is also 50.0 m/s, the same as the first wave.

Question 14

The superposition principle has to do with which of the following?
A)effects of waves at great distances
B)the ability of some waves to move very far
C)how displacements of interacting waves add together
D)relativistic wave behavior

Accepted Answer

The superposition principle states that when two or more waves interact, the net displacement is the sum of the individual displacements of the waves. This principle is important in understanding many aspects of wave behavior, including constructive and destructive interference.

Question 15

If a wave pulse is reflected from a free boundary, which of the following choices best describes what happens to the reflected pulse?
A)becomes inverted
B)remains upright
C)halved in amplitude
D)doubled in amplitude

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 16

Tripling the mass per unit length of a guitar string will result in changing the wave speed in the string by what factor?
A)0.58
B)1.00 (i.e., no change)
C)1.73
D)3.00

Accepted Answer

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

Question 17

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?
A)140 cm
B)100 cm
C)70 cm
D)Information about the amplitudes needs to be given to find an answer.

Accepted Answer

The answer of Two water waves meet at the same...

Question 18

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?
A)0
B)1
C)2
D)4

Accepted Answer

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

Question 19

For a wave traveling in a string, by what factor would the tension need to be increased to double the wave speed?
A)1.4
B)2.0
C)4.0
D)16

Accepted Answer

The wave speed is directly proportional to the square root of the tension in the string. Therefore, to double the wave speed, the tension must be increased by a factor of four. (Wave speed ∝ √Tension) Thus, the tension would need to be increased by a factor of 4, which is answer choice C.

Quiz 13: Vibrations and Waves

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?

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?

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

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.)

Two identical springs, each with spring constant k, are attached in parallel to a mass, which is then set into simple harmonic motion.What would be the spring constant of a single spring which would result in the same frequency of oscillation as the parallel springs?

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

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?

A pendulum on the Earth has a period T.The acceleration of due to gravity on Mars is less than that on the Earth, and the acceleration due to gravity on the Moon is even less.Where would the period of an identical pendulum be the least?

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.

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?

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?

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?

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?

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

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

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

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?

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

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.)