Question 1

A wave pulse travels along a string at a speed of 200 cm/s. If the string’s tension is doubled, what will be the new speed of the wave pulse?

Accepted Answer

$$v = 280 	ext{ cm/s}$$

Question 2

A stationary boat in the ocean is experiencing waves from a storm. The waves move at $$56 	ext{ km/h}$$ and have a wavelength of $$160 	ext{ m}. $$How much time elapses until the boat is first at the trough of a wave, starting from the crest?

Accepted Answer

$$5.1 	ext{ s}$$

Question 3

The displacement of a wave traveling in the positive x-direction is $$y(x, t) = (3.5 	ext{ cm}) 	imes \cos(2.7x - 92t). $$What is the frequency of this wave?

Accepted Answer

$$f = 14.6 	ext{ Hz}$$

Question 4

Refer to the snapshot graph of a wave at $$t = 0 	ext{ s} ($$see $$image_1). $$What is the amplitude of the wave?

Accepted Answer

$$4.0 	ext{ cm}$$

Question 5

Refer to the snapshot graph of a wave at $$t = 0 	ext{ s} ($$see $$image_1). $$What is the wavelength of the wave?

Accepted Answer

$$12 	ext{ m}$$

Question 6

Refer to the snapshot graph of a wave at $$t = 0 	ext{ s} ($$see $$image_1). If $$the wave speed is $$24 	ext{ m/s}$$, what is the frequency of the wave?

Accepted Answer

$$f = 2.0 	ext{ Hz}$$

Question 7

Refer to the history graph at $$x = 0 	ext{ m} of a $$wave moving to the right at $$2 	ext{ m/s} ($$see $$image_2). $$What is the amplitude of the wave?

Accepted Answer

$$6.0 	ext{ cm}$$

Question 8

Refer to the history graph at $$x = 0 	ext{ m} of a $$wave moving to the right at $$2 	ext{ m/s} ($$see $$image_2). $$What is the period of the wave?

Accepted Answer

$$T = 0.60 	ext{ s}$$

Question 9

Refer to the history graph at $$x = 0 	ext{ m} of a $$wave moving to the right at $$2 	ext{ m/s} ($$see $$image_2). $$What is the wavelength of the wave?

Accepted Answer

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

Question 10

A 2.0-m-long string is fixed at both ends and tightened until the wave speed is $$40 	ext{ m/s}. If $$the standing wave shown in $$image_5$$ has three full wavelengths on the string, what is the frequency of the standing wave?

Accepted Answer

$$f = 60 	ext{ Hz}$$

Question 11

A guitar string with a linear density of $$2.0 	ext{ g/m} is $$stretched between supports that are $$60 	ext{ cm}$$ apart. The string forms a standing wave with three antinodes when driven at $$420 	ext{ Hz}. $$What is the frequency of the fifth harmonic?

Accepted Answer

$$f_5 = 700$$ 	ext{ Hz}$$

Question 12

A guitar string with a linear density of $$2.0 	ext{ g/m} is $$stretched between supports that are $$60 	ext{ cm}$$ apart. The string forms a standing wave with three antinodes when driven at $$420 	ext{ Hz}. $$What is the tension in the string?

Accepted Answer

$$T = 56 	ext{ N}$$

Question 13

If a small wave pulse and a large wave pulse approach each other on a string, what happens after they meet and pass each other?

Accepted Answer

The large pulse continues unchanged, moving to the right.

Question 14

A wave pulse travels along a string at a speed of $$200 	ext{ cm/s}. If $$the string’s mass is quadrupled (but its length is unchanged), what will be the new speed?

Accepted Answer

$$v = 100 	ext{ cm/s}$$

Question 15

A wave pulse travels along a string at a speed of $$200 	ext{ cm/s}. If $$the string’s length is quadrupled (but its mass is unchanged), what will be the new speed?

Accepted Answer

$$v = 400 	ext{ cm/s}$$

Question 16

A wave pulse travels along a string at a speed of $$200 	ext{ cm/s}. If $$both the string’s mass and length are quadrupled, what will be the new speed?

Accepted Answer

$$v = 200 	ext{ cm/s}$$

Question 17

The principle of superposition states that when two waves overlap, the net displacement is:

Accepted Answer

The sum of the individual displacements.

Question 18

Refer to the sequence of snapshot graphs (see $$image_4) $$for two wave pulses approaching each other at $$1 	ext{ m/s}. $$What is the displacement at $$x = 5.0 	ext{ m} at$$ $$t = 3 	ext{ s}$$?

Accepted Answer

$$y = 0 	ext{ cm}$$

Traveling and Standing Waves: Step-by-Step Physics Guidance

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