Q: A wave on a string has a frequency of $$120 \ \mathrm{Hz}$$ and a wavelength of $$2.5 \ \mathrm{m}. $$What is its speed?

$$v = 120 \times 2.5 = 300 \ \mathrm{m/s}$$

Question 1

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

Accepted Answer

Transverse waves oscillate perpendicular to the direction of propagation, while longitudinal waves oscillate parallel to the direction of propagation.

Question 2

A metal guitar string has a linear density of $$\mu = 1.32 \ \mathrm{g/cm}. If $$the tension in the string is $$900 \ \mathrm{N}$$, what is the speed of a transverse wave on the string?

Accepted Answer

$$v = \sqrt{\dfrac{F_T}{\mu}} = \sqrt{\dfrac{900}{0.132}} = 53 \ \mathrm{m/s}$$

Question 3

Which equation correctly relates the speed $$v$$, wavelength $$\lambda$$, and frequency $$f of a $$periodic wave?

Accepted Answer

$$v = \lambda f$$

Question 4

A sensor on Mars is placed $$2000 \ \mathrm{m}$$ from a drilling operation. P-waves are detected at $$0.87 \ \mathrm{s}$$ and S-waves at $$1.67 \ \mathrm{s}. $$What is the speed of the P-waves?

Accepted Answer

$$v = \dfrac{2000}{0.87} = 2299 \ \mathrm{m/s}$$

Question 5

Which of the following is a correct formula for the speed of sound in a fluid?

Accepted Answer

$$v = \sqrt{\dfrac{B}{\rho}}$$

Question 6

If the speed of sound in air at $$20^\circ \mathrm{C} is$$ $$343 \ \mathrm{m/s}$$, what is the approximate speed at $$0^\circ \mathrm{C}$$?

Accepted Answer

$$v = 331 \ \mathrm{m/s}$$

Question 7

Which of the following best describes constructive interference?

Accepted Answer

When two waves meet and their amplitudes add, resulting in a larger amplitude.

Question 8

A standing wave is formed on a string of length $$L$$ fixed at both ends. What is the wavelength of the $$Nth $$harmonic?

Accepted Answer

$$\lambda_N = \dfrac{2L}{N}$$

Question 9

Which of the following is the correct formula for the fundamental frequency of a string fixed at both ends?

Accepted Answer

$$f_1$$ = \dfrac{v}{2L}$$

Question 10

Which property of a wave determines its pitch in sound?

Accepted Answer

Frequency

Question 11

A wave on a string has a frequency of $$120 \ \mathrm{Hz}$$ and a wavelength of $$2.5 \ \mathrm{m}. $$What is its speed?

Accepted Answer

$$v = 120 	imes 2.5 = 300 \ \mathrm{m/s}$$

Question 12

Which of the following is true about P-waves and S-waves in earthquakes?

Accepted Answer

P-waves are longitudinal and travel faster than S-waves.

Question 13

The audible range of human hearing is approximately:

Accepted Answer

$$20 \ \mathrm{Hz} to$$ $$20,000 \ \mathrm{Hz}$$

Question 14

Which equation gives the speed of a transverse wave on a string in terms of tension $$F_T$$ and linear mass density $$\mu$$?

Accepted Answer

$$v = \sqrt{\dfrac{F_T}{\mu}}$$

Question 15

A sound wave travels through air at $$20^\circ \mathrm{C}$$ with a speed of $$343 \ \mathrm{m/s}. If $$the frequency is $$686 \ \mathrm{Hz}$$, what is the wavelength?

Accepted Answer

$$\lambda = \dfrac{343}{686} = 0.5 \ \mathrm{m}$$

Question 16

Which of the following best describes the effect of increasing the tension in a guitar string on the speed of waves traveling through it?

Accepted Answer

The speed increases because $$v \propto \sqrt{F_T}.$$

Question 17

A standing wave on a string has three antinodes. What is the harmonic number and the wavelength?

Accepted Answer

Harmonic number $$N = 3$$, $$\lambda = \dfrac{2L}{3}$$

Question 18

Which formula gives the speed of sound in a gas as a function of temperature $$T (in $$Kelvin)?

Accepted Answer

$$v = v_0$ \sqrt{\dfrac{T}{T_0$}}$$

Question 19

If the speed of light in air is $$3 	imes 10^8$ \ \mathrm{m/s}$$, what is the frequency of visible light with a wavelength of $$500 \ \mathrm{nm}$$?

Accepted Answer

$$f = \dfrac{3 	imes 10^8$}{500 	imes 10$$^{-9}$$} = 6 	imes 10$$^{14}$$ \ \mathrm{Hz}$$

Mechanical Waves and Sound: Principles, Types, and Applications

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