Question 1

A sinusoidal wave is described by $$y(x,t) = A \cos(kx - \omega t). If $$the wave travels in the +x direction, what is the correct expression for the wave number $$k in $$terms of wavelength $$\lambda$$?

Accepted Answer

$$k = 2\pi / \lambda$$

Question 2

A string is fixed at both ends and has length $$L. $$What is the wavelength $$\$$lambda_2$$ of the second harmonic (first overtone) standing wave?

Accepted Answer

Question 3

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

Accepted Answer

The speed doubles.

Question 4

A wave pulse traveling toward a fixed end of a string is reflected. What happens to the pulse upon reflection?

Accepted Answer

The pulse inverts as it reflects.

Question 5

Two wave pulses pass each other on a string. One pulse has positive amplitude, the other has equal negative amplitude. What happens when they overlap?

Accepted Answer

Destructive interference occurs.

Question 6

For a standing wave on a string fixed at both ends, what is the condition for nodes?

Accepted Answer

$$x = n\lambda/2$$ where $$n = 0, 1, 2, ...$$

Question 7

A violin string vibrates at its fundamental frequency. If the string length is $$L$$ and the speed of the wave is $$v$$, what is the fundamental frequency $$f_1$$?

Accepted Answer

$$f_1 = v / 2L$

Question 8

A standing wave is established on a string fixed at both ends. If the string is vibrating at its fundamental frequency, how is the length of the string $$L$$ related to the wavelength $$\lambda$$?

Accepted Answer

L is equal to one-half of a wavelength

Question 9

A string of length $$L = 0.33 m $$produces a standing wave with a fundamental frequency of $$659 Hz $$and a wavelength of $$0.66 m. $$What is the speed $$v of $$the wave?

Accepted Answer

$$v = 435 m/s$$

Question 10

The principle of superposition states that when two or more waves overlap, the total displacement is:

Accepted Answer

The sum of the displacements of the individual waves

Question 11

A string is fixed at both ends and supports a standing wave. If the third harmonic is excited, how many nodes (including the ends) are present?

Accepted Answer

4 nodes

Question 12

If the mass per unit length $$\mu of a $$string is doubled, but the tension $$F$$ remains constant, what happens to the speed $$v of a $$transverse wave?

Accepted Answer

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

Question 13

A pulse traveling toward a free end of a string is reflected. What happens to the pulse upon reflection?

Accepted Answer

The pulse reflects without inverting.

Question 14

For a string fixed at both ends, the possible frequencies of standing waves are given by $$f_n = n v / 2L. $$What does $$n$$ represent?

Accepted Answer

The harmonic number (integer)

Question 15

A standing wave on a string is described by $$y(x,t) = (A_{sw} \sin kx) \sin \omega t. $$What is the amplitude at a node?

Accepted Answer

Zero amplitude

Question 16

A guitar string is plucked, producing a standing wave. Increasing the tension $$F in $$the string will:

Accepted Answer

Increase the frequency of the standing wave

Question 17

Which of the following best describes an antinode in a standing wave?

Accepted Answer

A point where the amplitude of string motion is greatest

Question 18

If a string fixed at both ends has length $$L$$ and supports a standing wave with $$n = 4$$, what is the wavelength $$\$$lambda_4$$?

Accepted Answer

$$\$$lambda_4$$ = L/4$$

Question 19

A string of length $$L is $$fixed at both ends. Which equation gives the possible wavelengths for standing waves?

Accepted Answer

$$\lambda_n = 2L/n$$

Mechanical Waves and Standing Waves on Strings

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