Question 1

When two identical wave pulses traveling toward each other on a string overlap, what happens to the displacement of the string at the point where they meet, according to the principle of superposition?

Accepted Answer

The displacement at the meeting point is the sum of the displacements of the two pulses.

Question 2

A wave pulse travels along a string with a speed $$v = 0.5\ \mathrm{cm/s}. If $$the pulse travels 6 cm, how long does it take?

Accepted Answer

$$t = 12\ \mathrm{s}$$

Question 3

Which of the following best describes a transverse wave?

Accepted Answer

A wave in which the particles of the medium move perpendicular to the direction of wave propagation.

Question 4

If the tension in a string is increased, what happens to the speed of a wave traveling on the string?

Accepted Answer

The speed increases.

Question 5

A string of length $$L = 1.6\ \mathrm{m} is $$fixed at both ends and supports a standing wave with 5 nodes. What is the wavelength $$\lambda of $$the standing wave?

Accepted Answer

$$\lambda = 0.8\ \mathrm{m}$$

Question 6

The speed of a wave on a string is given by $$v = \sqrt{\frac{T}{\mu}}. If $$the tension $$T is $$quadrupled, what happens to the wave speed?

Accepted Answer

The speed doubles.

Question 7

Which of the following statements about standing waves on a string with two fixed ends is correct?

Accepted Answer

Nodes are points of zero displacement, and anti-nodes are points of maximum displacement.

Question 8

A string has a linear mass density $$\mu = 0.015\ \mathrm{kg/m}$$ and tension $$T = 3.2\ \mathrm{N}. $$What is the speed of a wave on this string?

Accepted Answer

$$v = 14.6\ \mathrm{m/s}$$

Question 9

If you increase the frequency of oscillation for a standing wave on a string with fixed length, what happens to the number of nodes?

Accepted Answer

The number of nodes increases.

Question 10

Which of the following is true for a sinusoidal traveling wave on a string?

Accepted Answer

The speed of the wave depends on the tension and mass density of the string, not on the frequency.

Question 11

A standing wave on a string is shown in a snapshot graph. What does a history graph for a bead at a node look like?

Accepted Answer

A flat line at $$y = 0$$

Question 12

If two wave pulses of equal amplitude but opposite sign (one upward, one downward) overlap perfectly, what is the resulting displacement at the point of overlap?

Accepted Answer

Zero (complete destructive interference)

Question 13

A string of length $$L = 0.6\ \mathrm{m}$$ has two fixed ends and supports a standing wave in its fundamental mode. What is the wavelength $$\lambda of $$this mode?

Accepted Answer

$$\lambda = 1.2\ \mathrm{m}$$

Question 14

If the frequency of a traveling wave on a string is doubled but the tension and mass density remain constant, what happens to the wavelength?

Accepted Answer

The wavelength is halved.

Question 15

Which of the following best describes the relationship between the frequencies of the harmonics (modes) of a string fixed at both ends?

Accepted Answer

The frequency of the $$m-th $$mode is $$f_m = m f_1$, where f_1$ is the fundamental frequency.

Question 16

A string supports a standing wave with 4 nodes. If the tension in the string is decreased by half, what happens to the speed of the wave?

Accepted Answer

The speed decreases by a factor of $$1/\sqrt{2}.$$

Question 17

Which of the following is NOT a property of a standing wave on a string with two fixed ends?

Accepted Answer

All points on the string oscillate with the same amplitude.

Question 18

If a string is replaced with another string of higher linear mass density but the same tension, what happens to the wave speed?

Accepted Answer

The wave speed decreases.

Question 19

Which of the following is true about the motion of beads (points) on a string supporting a sinusoidal traveling wave?

Accepted Answer

Each bead oscillates with the same frequency but different phase.

Question 20

A standing wave is set up on a string with two fixed ends. If the string length is $$L$$ and the standing wave has $$n$$ nodes, what is the wavelength $$\lambda$$?

Accepted Answer

$$\lambda = \frac{2L}{n-1}$$

Quiz 5: Superposition of Wave Pulses and Predicting Resultant Motion

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