Q: A string of length $$L = 2.0\ \text{m}$$ and mass $$m = 0.10\ \text{kg} is $$under a tension of $$T_s = 50\ \text{N}. $$What is the speed of a wave on this string?

$$v = \sqrt{\frac{50}{0.05}} = 31.6\ \text{m/s}$$

Q: A sinusoidal wave has a frequency $$f = 200\ \text{Hz}$$ and a wavelength $$\lambda = 0.85\ \text{m}. $$What is the speed of the wave?

$$v = \lambda f = 0.85 \times 200 = 170\ \text{m/s}$$

Q: A sound wave in air at $$20^\circC $$has a speed of $$343\ \text{m/s}. If $$the frequency of the sound is $$686\ \text{Hz}$$, what is its wavelength?

$$\lambda = \frac{v}{f} = \frac{343}{686} = 0.5\ \text{m}$$

Question 1

Which of the following best describes a mechanical wave?

Accepted Answer

A disturbance that can travel through a material medium, transferring energy without transferring matter.

Question 2

A stadium crowd performs 'The Wave,' where people stand up and sit down as the wave moves horizontally. What type of wave is this an example of?

Accepted Answer

A transverse wave, because the displacement of people is perpendicular to the direction of wave travel.

Question 3

Which of the following actions will increase the speed of a wave traveling down a string?

Accepted Answer

Using a lighter string of the same length, under the same tension.

Question 4

The speed of a transverse wave on a string is given by $$v_{	ext{string}} = \sqrt{\frac{T_s}{\mu}}. If $$the tension $$T_s is $$quadrupled and the linear density $$\mu is $$doubled, what happens to the wave speed?

Accepted Answer

It increases by a factor of $$\sqrt{2}.$$

Question 5

A sound wave in air is an example of which type of wave?

Accepted Answer

A longitudinal mechanical wave.

Question 6

A string of length $$L = 2.0\ 	ext{m}$$ and mass $$m = 0.10\ 	ext{kg} is $$under a tension of $$T_s = 50\ 	ext{N}. $$What is the speed of a wave on this string?

Accepted Answer

$$v = \sqrt{\frac{50}{0.05}} = 31.6\ 	ext{m/s}$$

Question 7

Which of the following statements about wave speed is correct?

Accepted Answer

Wave speed depends only on the properties of the medium, not on the amplitude or frequency of the wave.

Question 8

A sinusoidal wave has a frequency $$f = 200\ 	ext{Hz}$$ and a wavelength $$\lambda = 0.85\ 	ext{m}. $$What is the speed of the wave?

Accepted Answer

$$v = \lambda f = 0.85 	imes 200 = 170\ 	ext{m/s}$$

Question 9

Which of the following best describes the principle of superposition?

Accepted Answer

The displacement at any point is the algebraic sum of the displacements due to each wave present.

Question 10

If two waves of equal amplitude and opposite phase meet at a point, what type of interference occurs?

Accepted Answer

Destructive interference.

Question 11

A sound wave in air at $$20^\circC $$has a speed of $$343\ 	ext{m/s}. If $$the frequency of the sound is $$686\ 	ext{Hz}$$, what is its wavelength?

Accepted Answer

$$\lambda = \frac{v}{f} = \frac{343}{686} = 0.5\ 	ext{m}$$

Question 12

Which of the following is NOT a property of a mechanical wave?

Accepted Answer

It can travel through a vacuum.

Question 13

A string has a linear density $$\mu = 0.02\ 	ext{kg/m}$$ and is under a tension $$T_s = 18\ 	ext{N}. $$What is the speed of a wave on this string?

Accepted Answer

$$v = \sqrt{\frac{18}{0.02}} = 30\ 	ext{m/s}$$

Question 14

Which of the following best describes the difference between transverse and longitudinal waves?

Accepted Answer

In transverse waves, particle displacement is perpendicular to wave direction; in longitudinal waves, it is parallel.

Question 15

A sinusoidal wave is described by the equation $$y(x, t) = A \sin(kx - \omega t). $$What does the parameter $$A$$ represent?

Accepted Answer

The amplitude, or maximum displacement from equilibrium.

Question 16

If the frequency of a wave is doubled while its speed remains constant, what happens to its wavelength?

Accepted Answer

It is halved.

Question 17

A wave pulse is sent down a rope attached to a wall. When the pulse reflects from the wall, what happens to its orientation?

Accepted Answer

It inverts (flips upside down).

Question 18

Which of the following is a correct statement about the relationship $$v = \lambda f$$?

Accepted Answer

It applies to both transverse and longitudinal sinusoidal waves.

Question 19

A string vibrates with a frequency of $$f = 275\ 	ext{Hz}$$ and a wavelength of $$\lambda = 0.0525\ 	ext{m}. $$What is the speed of the wave?

Accepted Answer

$$v = 0.0525 	imes 275 = 14.44\ 	ext{m/s}$$

Traveling Waves and Sound: The Wave Model, Properties, and Interference

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