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

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

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

For a mass-spring system, at what displacement $$x (as a $$fraction of amplitude $$A) is $$the mechanical energy 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 with a period determined by 10 oscillations in 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 $$1.25\ \mathrm{s}. $$What is the length $$L of $$the pendulum rod? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

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

Question 5

A wrecking ball swings on a $$13\ \mathrm{m}$$ 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 graph shows the intensity of a damped oscillation. If the time constant for the decay is $$1.9 	imes 10$$^{-3}$$\ \mathrm{s}$$, what is the frequency of oscillation?

Accepted Answer

$$f = 1.8\ \mathrm{kHz}$$

Question 7

A car of mass $$1500\ \mathrm{kg}$$ bounces with maximum amplitude on a washboard road with bumps $$5.8\ \mathrm{m}$$ apart at a speed of $$6.2\ \mathrm{m/s}. $$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 $$5000\ \mathrm{m/s}$$ and $$3000\ \mathrm{m/s}$$, 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 $$y(x, t) = (3.5\ \mathrm{cm}) \cos(2.7x - 92t). $$What is the frequency of this wave?

Accepted Answer

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

Question 10

A musical note $$C_6$$ has a frequency of $$1050\ \mathrm{Hz}. If a $$musician can identify this note after hearing 12 cycles, how much time does this correspond to?

Accepted Answer

$$t = 0.011\ \mathrm{s}$$

Question 11

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

Accepted Answer

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

Question 12

A rock band produces $$120\ \mathrm{dB} at$$ $$5.0\ \mathrm{m}$$ from the speaker. What is the sound intensity level at $$35\ \mathrm{m}$$ from the speaker?

Accepted Answer

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

Question 13

Two waves on a string are shown approaching each other at $$1\ \mathrm{m/s}. $$Which graph best represents the string at $$t = 2\ \mathrm{s}$$?

Accepted Answer

Image 8

Question 14

A standing wave on a string oscillates at $$100\ \mathrm{Hz}$$ and the distance between adjacent nodes is $$0.20\ \mathrm{m}. $$What is the wave speed?

Accepted Answer

$$v = 40\ \mathrm{m/s}$$

Question 15

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

Accepted Answer

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

Question 16

A flute plays $$440\ \mathrm{Hz}$$ and a second flute is slightly flat, producing 3 beats per second. What is the frequency of the second flute?

Accepted Answer

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

Question 17

A guitar string is $$64\ \mathrm{cm}$$ long, tension $$74\ \mathrm{N}$$, and is pressed at the center to give $$294\ \mathrm{Hz}. If $$the string is bent with a $$4.0\ \mathrm{N}$$ force moving it $$8.0\ \mathrm{mm}$$, what is the new frequency?

Accepted Answer

$$f_{new} = 310\ \mathrm{Hz}$$

Question 18

The rainbows from a DVD are more spread out than those from a CD. What does this tell you about the track spacing on DVDs compared to CDs?

Accepted Answer

DVDs have smaller track spacing than CDs.

Question 19

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

Accepted Answer

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

Question 20

A blue-ringed octopus has reflectin plates of thickness $$62\ \mathrm{nm}$$ and index $$n = 1.59. $$What is the longest wavelength in air for constructive interference?

Accepted Answer

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

Question 21

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

Accepted Answer

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

Physics Exam Review: Oscillations, Waves, Sound, and Light

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