Q: A sound has an intensity of $$1 \times 10$$^{-8}$$\ \mathrm{W/m^2$}. $$What is its sound level in decibels ($$\beta$$)? ($$I_0 = 1$$ \times $$10^{-12}$$\ \mathrm{$$W/m^2$$}$$)

$$\beta = 10 \log_{10}\left(\frac{1 \times 10$$^{-8}$$}{1 \times 10$$^{-12}$$}\right) = 10 \log_{10}(10^4$) = 40\ \mathrm{dB}$$

Q: A thin film of oil ($$n=1.4) $$floats on water ($$n=1.33). $$For constructive interference in reflected light (one phase shift), what is the minimum nonzero thickness $$t of $$the oil film for light of wavelength $$560\ \mathrm{nm} in $$air?

$$t = \frac{1}{4} \frac{\lambda}{n} = \frac{560}{4 \times 1.4} = 100\ \mathrm{nm}$$

Question 1

A sinusoidal wave on a string is described by $$y(x, t) = A \sin(kx - \omega t). If $$the wave has a frequency of $$10\ \mathrm{Hz}$$ and a wavelength of $$0.5\ \mathrm{m}$$, what is the speed of the wave?

Accepted Answer

$$v = 5\ \mathrm{m/s}$$

Question 2

A mass $$m is $$attached to a spring with spring constant $$k. If $$the mass is quadrupled, how does the period of oscillation change?

Accepted Answer

It doubles: $$T' = 2T$$

Question 3

A closed-open pipe has a length $$L = 0.85\ \mathrm{m}. $$What is the wavelength of the second harmonic?

Accepted Answer

$$\lambda = \frac{4L}{3} = 1.13\ \mathrm{m}$$

Question 4

The speed of a wave on a string is given by $$v = \sqrt{\frac{T}{\mu}}. If $$the tension $$T is $$quadrupled while the mass per unit length $$\mu$$ remains constant, what happens to the wave speed?

Accepted Answer

It doubles

Question 5

A car horn emits a sound at $$500\ \mathrm{Hz}. If $$the car moves toward a stationary observer at $$30\ \mathrm{m/s} ($$speed of sound $$v = 340\ \mathrm{m/s}$$), what frequency does the observer hear?

Accepted Answer

$$f' = 500 \frac{340 + 30}{340} \approx 544\ \mathrm{Hz}$$

Question 6

If the intensity of a sound at a distance $$r$$ from the source is $$I$$, what will be the intensity at a distance $$2r$$ from the same source (assuming spherical spreading)?

Accepted Answer

$$I/4$$

Question 7

A sound has an intensity of $$1 	imes 10$$^{-8}$$\ \mathrm{W/m^2$}. $$What is its sound level in decibels ($$\beta$$)? ($$I_0 = 1$$ 	imes $$10^{-12}$$\ \mathrm{$$W/m^2$$}$$)

Accepted Answer

$$\beta = 10 \log_{10}\left(\frac{1 	imes 10$$^{-8}$$}{1 	imes 10$$^{-12}$$}ight) = 10 \log_{10}(10^4$) = 40\ \mathrm{dB}$$

Question 8

Two tuning forks produce frequencies of $$256\ \mathrm{Hz}$$ and $$260\ \mathrm{Hz}$$ when sounded together. What is the beat frequency?

Accepted Answer

$$4\ \mathrm{Hz}$$

Question 9

In a double-slit experiment, the distance between the slits is doubled while all other parameters remain constant. What happens to the fringe spacing on the screen?

Accepted Answer

It halves

Question 10

A light wave travels from air ($$n=1.0) $$into glass ($$n=1.5). $$Which of the following quantities remains unchanged?

Accepted Answer

Frequency

Question 11

A thin film of oil ($$n=1.4) $$floats on water ($$n=1.33). $$For constructive interference in reflected light (one phase shift), what is the minimum nonzero thickness $$t of $$the oil film for light of wavelength $$560\ \mathrm{nm} in $$air?

Accepted Answer

$$t = \frac{1}{4} \frac{\lambda}{n} = \frac{560}{4 	imes 1.4} = 100\ \mathrm{nm}$$

Question 12

A standing wave is formed on a string fixed at both ends. If the string length is $$L$$ and the third harmonic is excited, what is the wavelength of the standing wave?

Accepted Answer

$$\lambda = \frac{2L}{3}$$

Question 13

A sound source emits a constant power $$P. If $$you move from $$2\ \mathrm{m} to$$ $$6\ \mathrm{m}$$ away from the source, by what factor does the intensity decrease?

Accepted Answer

By a factor of $$\left(\frac{2}{6}\$$right)^2$$ = \frac{1}{9}$$

Question 14

Which of the following best describes resonance in a physical system?

Accepted Answer

When the driving frequency matches the natural frequency of the system

Question 15

In a single-slit diffraction experiment, what happens to the width of the central maximum if the slit width is decreased?

Accepted Answer

It increases

Question 16

A pendulum has a length $$L$$ and period $$T. If $$the pendulum is taken to a planet where the acceleration due to gravity is four times that on Earth, what happens to the period?

Accepted Answer

It halves: $$T' = \frac{T}{2}$$

Question 17

Two waves with path difference $$\Delta L = (n + \frac{1}{2})\lambda$$ meet at a point. What type of interference occurs?

Accepted Answer

Destructive interference

Question 18

A laser beam in air ($$n=1.0) $$enters water ($$n=1.33) at an $$angle. If the wavelength in air is $$600\ \mathrm{nm}$$, what is the wavelength in water?

Accepted Answer

$$\lambda_{water} = \frac{\lambda_{air}}{n} = \frac{600}{1.33} \approx 451\ \mathrm{nm}$$

Question 19

A string has a mass per unit length $$\mu = 0.01\ \mathrm{kg/m}$$ and is under a tension of $$T = 100\ \mathrm{N}. $$What is the speed of a wave on this string?

Accepted Answer

$$v = \sqrt{\frac{100}{0.01}} = 100\ \mathrm{m/s}$$

Waves, Sound, and Light: Comprehensive Study Guide

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