Q: The intensity of a cricket's chirp decays as a damped oscillation. If the frequency is $$f = 5.0\ \mathrm{Hz}$$ and the time constant is $$\tau = 1.9 \times 10$$^{-3}$$\ \mathrm{s}$$, what is the equation for the intensity as a function of time?

$$I(t) = I_0$ e$$^{-t/\tau}$$ \cos(2\pi f t)$$

Q: A child’s ear canal is 1.3 cm long. At what frequencies in the audible range will the child have increased hearing sensitivity (resonance)? (Speed of sound in air $$v = 343\ \mathrm{m/s})$$

$$f = 6700\ \mathrm{Hz},\ 2.0 \times 10^4$\ \mathrm{Hz}$$

Q: A laser of wavelength 632 nm passes through muscle tissue with striations ranging from 1.87 to 1.94 $$\mum. If $$the screen is 30 cm behind the fish, what is the distance spanned by the diffraction spot as it moves back and forth?

$$\Delta y = 3.0 \times 10$$^{-3}$$\ \mathrm{m}$$

Q: A 690 nm laser creates a diffraction pattern on a screen 30 cm from fog droplets. If the central maximum is 0.24 cm in diameter, what is the diameter of the droplet?

$$D = 2.1 \times 10$$^{-4}$$\ \mathrm{m}$$

Question 1

A mass attached to a spring oscillates with amplitude $$A. $$When the displacement is $$\frac{1}{2}A$$, what fraction of the total mechanical energy is kinetic energy?

Accepted Answer

$$\frac{3}{4}$$

Question 2

At what displacement $$x (as a $$fraction of amplitude $$A) is $$the mechanical energy of a mass-spring system half kinetic and half potential?

Accepted Answer

$$x = 0.71A$$

Question 3

A 120 g air-track glider is attached to a spring and oscillates. If 10 oscillations take 18.5 s, what is the spring constant $$k$$?

Accepted Answer

$$k = 1.4\ \mathrm{N/m}$$

Question 4

A pendulum completes one full oscillation in 1.25 s. What is the length of the pendulum rod? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$L = 0.388\ \mathrm{m}$$

Question 5

A wrecking ball swings on a 13-m-long cable. If released from rest, how much time do you have to move out of the way before it reaches the lowest point?

Accepted Answer

$$t = 1.81\ \mathrm{s}$$

Question 6

The intensity of a cricket's chirp decays as a damped oscillation. If the frequency is $$f = 5.0\ \mathrm{Hz}$$ and the time constant is $$	au = 1.9 	imes 10$$^{-3}$$\ \mathrm{s}$$, what is the equation for the intensity as a function of time?

Accepted Answer

$$I(t) = I_0$ e$$^{-t/	au}$$ \cos(2\pi f t)$$

Question 7

A car of mass 1500 kg bounces with maximum amplitude on a washboard road with bumps 5.8 m apart at a speed of 6.2 m/s. What is the spring constant of the car’s springs?

Accepted Answer

$$k = 68\ \mathrm{N/m}$$

Question 8

An earthquake 60 km from a city produces P and S waves that travel at 5000 m/s and 3000 m/s, respectively. How much time after the P wave does the S wave arrive?

Accepted Answer

$$\Delta t = 8.0\ \mathrm{s}$$

Question 9

A wave is described by $$y(x, t) = (3.5\ \mathrm{cm}) \cos(2.7x - 92t)$$, where $$x is in $$meters and $$t in $$seconds. What is the frequency of this wave?

Accepted Answer

$$f = 15\ \mathrm{Hz}$$

Question 10

For the same wave $$y(x, t) = (3.5\ \mathrm{cm}) \cos(2.7x - 92t)$$, what is the wavelength?

Accepted Answer

$$\lambda = 2.3\ \mathrm{m}$$

Question 11

A solar cooker with a 1.4-m-diameter dish focuses sunlight onto a pot with a 25-cm diameter. If the intensity of sunlight is $$1000\ \mathrm{W/m^2$}$$, what is the total solar power captured by the dish?

Accepted Answer

$$P = 1500\ \mathrm{W}$$

Question 12

A rock band produces a sound intensity level of 120 dB at 5.0 m from the speaker. What is the sound intensity level at 35 m from the speaker?

Accepted Answer

$$\beta = 100\ \mathrm{dB}$$

Question 13

A child’s ear canal is 1.3 cm long. At what frequencies in the audible range will the child have increased hearing sensitivity (resonance)? (Speed of sound in air $$v = 343\ \mathrm{m/s})$$

Accepted Answer

$$f = 6700\ \mathrm{Hz},\ 2.0 	imes 10^4$\ \mathrm{Hz}$$

Question 14

Two flutes play the note A (440 Hz). One flute is slightly flat, and three beats per second are heard. What is the frequency of the flat flute?

Accepted Answer

$$f = 437\ \mathrm{Hz}$$

Question 15

A guitar string is 64 cm long and has a tension of 74 N. When pressed at the center fret, it vibrates at 294 Hz. If the string is bent with a force of 4.0 N, increasing its length by 8.0 mm, what happens to the frequency?

Accepted Answer

The frequency increases to $$f_{new} = 310\ \mathrm{Hz}$$

Question 16

If the light spectrum reflected from a DVD is more spread out than from a CD, what does this indicate about the track spacing?

Accepted Answer

The DVD has smaller track spacing than the CD.

Question 17

Light of wavelength 500 nm and an unknown wavelength illuminate a double slit. The 10th bright fringe of the unknown wavelength overlaps the 8th bright fringe of the 500 nm light. What is the unknown wavelength?

Accepted Answer

$$\lambda' = 400\ \mathrm{nm}$$

Question 18

A laser of wavelength 632 nm passes through muscle tissue with striations ranging from 1.87 to 1.94 $$\mum. If $$the screen is 30 cm behind the fish, what is the distance spanned by the diffraction spot as it moves back and forth?

Accepted Answer

$$\Delta y = 3.0 	imes 10$$^{-3}$$\ \mathrm{m}$$

Question 19

A blue-ringed octopus has reflectin plates with thickness 62 nm and index of refraction $$n = 1.59. $$What is the longest wavelength in air that will give constructive interference from opposite sides of the plates?

Accepted Answer

$$\lambda_{air} = 390\ \mathrm{nm}$$

Question 20

A 690 nm laser creates a diffraction pattern on a screen 30 cm from fog droplets. If the central maximum is 0.24 cm in diameter, what is the diameter of the droplet?

Accepted Answer

$$D = 2.1 	imes 10$$^{-4}$$\ \mathrm{m}$$

Oscillations, Waves, and Sound: Step-by-Step Physics Guidance

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