Q: A sound wave travels through air with a frequency of $$440\ \mathrm{Hz}$$ and a wavelength of $$0.78\ \mathrm{m}. $$What is the speed of sound in air based on these values?

$$v = f \lambda = 440 \times 0.78 = 343.2\ \mathrm{m/s}$$

Q: A guitar string $$0.65\ \mathrm{m}$$ long vibrates at its fundamental frequency with a wave speed of $$520\ \mathrm{m/s}. $$What is the fundamental frequency?

$$f_1$$ = \frac{v}{2L} = \frac{520}{2 \times 0.65} = 400\ \mathrm{Hz}$$

Q: A student observes two sound waves with frequencies $$f_1 = 256$$\ \mathrm{Hz}$$ and f_2$ = 260\ \mathrm{Hz}$$ interfering. What is the beat frequency?

$$f_{\text{beat}} = |f_1$ - f_2$| = |256 - 260| = 4\ \mathrm{Hz}$$

Q: A pipe open at both ends has a length of $$1.2\ \mathrm{m}. $$What is the wavelength of the fundamental mode?

$$\lambda = 2L = 2 \times 1.2 = 2.4\ \mathrm{m}$$

Q: A sound source emits a frequency $$f = 500\ \mathrm{Hz}$$ and moves toward a stationary observer at $$v_s = 30\ \mathrm{m/s}. If $$the speed of sound is $$v = 340\ \mathrm{m/s}$$, what is the observed frequency?

$$f' = \frac{v}{v - v_s} f = \frac{340}{340 - 30} \times 500 = 545\ \mathrm{Hz}$$

Q: A $$2.0\ \mathrm{kg}$$ block of aluminum ($$c = 900\ \mathrm{J/kg\cdot K}) is $$heated from $$20^{\circ}$$\mathrm{C}$$ to 50$$^{\circ}$$\mathrm{C}. $$How much heat energy is required?

$$Q = mc\Delta T = 2.0 \times 900 \times (50 - 20) = 54,000\ \mathrm{J}$$

Question 1

Which of the following statements best distinguishes a mechanical wave from an electromagnetic wave?

Accepted Answer

A mechanical wave requires a medium to propagate, while an electromagnetic wave does not.

Question 2

A sound wave travels through air with a frequency of $$440\ \mathrm{Hz}$$ and a wavelength of $$0.78\ \mathrm{m}. $$What is the speed of sound in air based on these values?

Accepted Answer

$$v = f \lambda = 440 	imes 0.78 = 343.2\ \mathrm{m/s}$$

Question 3

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

Accepted Answer

In longitudinal waves, particle vibration is parallel to wave propagation; in transverse waves, it is perpendicular.

Question 4

A guitar string $$0.65\ \mathrm{m}$$ long vibrates at its fundamental frequency with a wave speed of $$520\ \mathrm{m/s}. $$What is the fundamental frequency?

Accepted Answer

$$f_1$$ = \frac{v}{2L} = \frac{520}{2 	imes 0.65} = 400\ \mathrm{Hz}$$

Question 5

Which equation correctly relates the frequency $$f$$ and period $$T of a $$wave?

Accepted Answer

$$f = \frac{1}{T}$$

Question 6

A student observes two sound waves with frequencies $$f_1 = 256$$\ \mathrm{Hz}$$ and f_2$ = 260\ \mathrm{Hz}$$ interfering. What is the beat frequency?

Accepted Answer

$$f_{	ext{beat}} = |f_1$ - f_2$| = |256 - 260| = 4\ \mathrm{Hz}$$

Question 7

Which of the following best describes constructive interference?

Accepted Answer

When two waves meet in phase and their amplitudes add to produce a larger displacement.

Question 8

A pipe open at both ends has a length of $$1.2\ \mathrm{m}. $$What is the wavelength of the fundamental mode?

Accepted Answer

$$\lambda = 2L = 2 	imes 1.2 = 2.4\ \mathrm{m}$$

Question 9

A sound source emits a frequency $$f = 500\ \mathrm{Hz}$$ and moves toward a stationary observer at $$v_s = 30\ \mathrm{m/s}. If $$the speed of sound is $$v = 340\ \mathrm{m/s}$$, what is the observed frequency?

Accepted Answer

$$f' = \frac{v}{v - v_s} f = \frac{340}{340 - 30} 	imes 500 = 545\ \mathrm{Hz}$$

Question 10

Which of the following statements about standing waves is correct?

Accepted Answer

Standing waves are formed by the interference of two waves of equal amplitude and frequency traveling in opposite directions.

Question 11

A $$2.0\ \mathrm{kg}$$ block of aluminum ($$c = 900\ \mathrm{J/kg\cdot K}) is $$heated from $$20^{\circ}$$\mathrm{C}$$ to 50$$^{\circ}$$\mathrm{C}. $$How much heat energy is required?

Accepted Answer

$$Q = mc\Delta T = 2.0 	imes 900 	imes (50 - 20) = 54,000\ \mathrm{J}$$

Question 12

Which law states that if two objects are each in thermal equilibrium with a third object, then they are in thermal equilibrium with each other?

Accepted Answer

Zeroth Law of Thermodynamics

Question 13

A $$0.5\ \mathrm{kg}$$ sample of ice at $$0^{\circ}$$\mathrm{C}$$ is melted to water at 0$$^{\circ}$$\mathrm{C}. $$What is the energy required? (Latent heat of fusion for ice $$L_f = 334\ \mathrm{kJ/kg})$$

Accepted Answer

$$Q = mL_f = 0.5 	imes 334,000 = 167,000\ \mathrm{J}$$

Question 14

Which of the following best explains why metals feel colder than wood at the same temperature?

Accepted Answer

Metals have higher thermal conductivity, so they transfer heat away from your hand faster.

Question 15

A light ray passes from air ($$n_1 = 1.0$) into glass (n_2$ = 1.5) at an $$incident angle of $$30^{\circ}. $$What is the angle of refraction?

Accepted Answer

$$n_1$$ \sin \$$theta_1$$ = $$n_2$$ \sin \$$theta_2$$ \Rightarrow \sin \$$theta_2$$ = \frac{$$n_1$$}{$$n_2$$} \sin \$$theta_1$$ = \frac{1.0}{1.5} \sin $$30^{\circ} = 0.333$, so $$\$$theta_2$$ = $$19.5^{\circ}$$

Question 16

Which of the following is true about the Doppler effect for sound?

Accepted Answer

The observed frequency increases if the source moves toward the observer.

Question 17

A $$100\ \mathrm{W}$$ sound source emits energy uniformly in all directions. What is the intensity at a distance of $$5\ \mathrm{m}$$ from the source?

Accepted Answer

$$I = \frac{P}{4\pi r^2$} = \frac{100}{4\pi (5)^2$} = 0.318\ \mathrm{W/m^2$}$$

Question 18

Which of the following best describes the relationship between frequency and wavelength for electromagnetic waves in a vacuum?

Accepted Answer

$$c = f \lambda$$, where $$c is $$the speed of light.

Waves and Thermodynamics: Physics with Calculus Study Notes

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