Q: For a diffraction grating with slit separation $$d$$, at what angles $$\theta$$ will the principal maxima (bright fringes) appear for light of wavelength $$\lambda$$?

$$\sin \theta = m \frac{\lambda}{d}$$, where $$m = 0, 1, 2, ...$$

Q: A diffraction grating has slit spacing $$d = 5.00\ \mu\mathrm{m}$$ and is illuminated with yellow light of wavelength $$\lambda = 570\ \mathrm{nm}. $$What is the angle $$\theta$$ for the third-order bright fringe?

$$\theta = \arcsin\left(3 \frac{570 \times 10$$^{-9}$$}{5.00 \times 10$$^{-6}$$}\right)$$

Question 1

Which of the following best describes a wavefront in the context of two-dimensional surface waves?

Accepted Answer

A curve or surface on which all points have the same phase.

Question 2

A stone is dropped into a still pond, creating circular ripples. If the energy of the wavefront is $$E$$, what is the energy per unit length at a distance $$r$$ from the source?

Accepted Answer

$$\frac{E}{2\pi r}$$

Question 3

For a spherical wave spreading out in three dimensions, how does the amplitude $$A of $$the wave depend on the distance $$r$$ from the source?

Accepted Answer

$$A \propto \frac{1}{r}$$

Question 4

Which of the following statements about sound waves is correct?

Accepted Answer

Sound waves are longitudinal waves that can travel through solids, liquids, and gases.

Question 5

The speed of sound in dry air at $$20^\circC is $$closest to:

Accepted Answer

$$343\ \mathrm{m/s}$$

Question 6

A point source emits sound uniformly in all directions with a power output $$P_s. $$What is the intensity $$I at a $$distance $$r$$ from the source?

Accepted Answer

$$I = \frac{P_s}{4\pi r^2$}$$

Question 7

The intensity level $$\beta in $$decibels (dB) is given by which formula?

Accepted Answer

$$\beta = (10\ \mathrm{dB}) \log \left( \frac{I}{I_{th}} \right)$$

Question 8

Two violinists play notes at $$350\ \mathrm{Hz}$$ and $$353\ \mathrm{Hz}$$ simultaneously. What is the beat frequency heard by an observer?

Accepted Answer

$$3\ \mathrm{Hz}$$

Question 9

A car horn emits a frequency $$f_s = 400\ \mathrm{Hz} as it $$approaches a stationary observer at $$v_s = 30\ \mathrm{m/s}. If $$the speed of sound is $$c = 343\ \mathrm{m/s}$$, what frequency does the observer hear?

Accepted Answer

$$f_o = f_s \frac{c}{c - v_s}$$

Question 10

Which of the following best describes the Doppler effect?

Accepted Answer

A change in the observed frequency of a wave due to the relative motion of the source and observer.

Question 11

If two coherent sources are separated by a distance $$d$$ and emit waves of wavelength $$\lambda$$, what is the maximum number of nodal lines on one side of the line joining the sources?

Accepted Answer

The greatest integer less than or equal to $$2\left(\frac{d}{\lambda}\right)$$

Question 12

According to Huygens’ principle, what happens when a wavefront encounters a barrier with a small opening (width less than the wavelength)?

Accepted Answer

The wave spreads out significantly after passing through the opening (diffraction).

Question 13

For a diffraction grating with slit separation $$d$$, at what angles $$	heta$$ will the principal maxima (bright fringes) appear for light of wavelength $$\lambda$$?

Accepted Answer

$$\sin 	heta = m \frac{\lambda}{d}$$, where $$m = 0, 1, 2, ...$$

Question 14

A diffraction grating has slit spacing $$d = 5.00\ \mu\mathrm{m}$$ and is illuminated with yellow light of wavelength $$\lambda = 570\ \mathrm{nm}. $$What is the angle $$	heta$$ for the third-order bright fringe?

Accepted Answer

$$	heta = \arcsin\left(3 \frac{570 	imes 10$$^{-9}$$}{5.00 	imes 10$$^{-6}$$}ight)$$

Question 15

Which of the following is a correct statement about X-ray diffraction?

Accepted Answer

X-rays have wavelengths on the order of atomic spacings and can be used to study crystal structures.

Question 16

A sound wave has an intensity of $$1.50\ \mathrm{W/m^2$} at a $$distance of $$2.60\ \mathrm{m}$$ from a point source. What is the power output $$P of $$the source?

Accepted Answer

$$P = I 	imes 4\pi r^2$ = 1.50 	imes 4\pi (2.60)^2$

Question 17

If a source moves at speed $$v_s$$ greater than the speed of sound $$c$$, what type of wave phenomenon is observed?

Accepted Answer

Shock waves

Question 18

The Mach number is defined as:

Accepted Answer

$$	ext{Mach number} = \frac{v_s}{c}$$

Waves in Two and Three Dimensions: Study Notes for Physics with Calculus

Study Guide - Practice Questions

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