Q: If the intensity of a sound increases from $$1.0 \times 10$$^{-12}$$\ \mathrm{W/m^2$} to$$ $$1.0 \times 10$$^{-8}$$\ \mathrm{W/m^2$}$$, by how many decibels does the sound level increase?

$$\Delta \beta = 10 \log_{10}\left(\frac{1.0 \times 10$$^{-8}$$}{1.0 \times 10$$^{-12}$$}\right) = 40\ \mathrm{dB}$$

Question 1

A 2.0 m long copper wire has a cross-sectional area of $$1.0 	imes 10$$^{-6}$$ \ \mathrm{m}^2$$ and a resistivity $$ho = 1.7 	imes 10$$^{-8}$$ \ \Omega \cdot \mathrm{m}. $$What is the resistance of the wire?

Accepted Answer

$$R = \rho \frac{\ell}{A} = 0.034\ \Omega$$

Question 2

Three resistors, $$R_1 = 2$$\ \Omega$$, R_2$ = 4\ \Omega$$, and $$R_3 = 6$$\ \Omega$$, are connected in series. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = R_1$ + R_2$ + R_3$ = 12\ \Omega$$

Question 3

A mass $$m$$ attached to a spring with spring constant $$k$$ oscillates with amplitude $$A. $$What is the maximum speed of the mass during its motion?

Accepted Answer

$$v_{max} = A \sqrt{\frac{k}{m}}$$

Question 4

A sound wave travels through air at $$v = 340\ \mathrm{m/s}. If $$its frequency is $$1700\ \mathrm{Hz}$$, what is its wavelength?

Accepted Answer

$$\lambda = \frac{v}{f} = 0.2\ \mathrm{m}$$

Question 5

A 0.5 kg mass is attached to a spring with $$k = 200\ \mathrm{N/m}. $$What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}} = 0.314\ \mathrm{s}$$

Question 6

A string of length $$2.0\ \mathrm{m}$$ and mass $$0.10\ \mathrm{kg} is $$under a tension of $$50\ \mathrm{N}. $$What is the speed of a wave on the string?

Accepted Answer

$$v = \sqrt{\frac{T \ell}{m}} = 31.6\ \mathrm{m/s}$$

Question 7

A 60 W light bulb emits sound isotropically. What is the intensity at a distance of $$10\ \mathrm{m}$$ from the bulb?

Accepted Answer

$$I = \frac{P}{4\pi r^2$} = 0.048\ \mathrm{W/m^2$}$$

Question 8

If the intensity of a sound increases from $$1.0 	imes 10$$^{-12}$$\ \mathrm{W/m^2$} to$$ $$1.0 	imes 10$$^{-8}$$\ \mathrm{W/m^2$}$$, by how many decibels does the sound level increase?

Accepted Answer

$$\Delta \beta = 10 \log_{10}\left(\frac{1.0 	imes 10$$^{-8}$$}{1.0 	imes 10$$^{-12}$$}ight) = 40\ \mathrm{dB}$$

Question 9

A circuit contains a $$12\ \Omega$$ resistor and a $$6\ \Omega$$ resistor in parallel. What is the equivalent resistance?

Accepted Answer

$$\frac{1}{R_{eq}} = \frac{1}{12} + \frac{1}{6} \Rightarrow R_{eq} = 4\ \Omega$$

Question 10

A mass on a spring oscillates according to $$x(t) = 0.10 \cos(2\pi 	imes 5 t). $$What is the amplitude and frequency of the motion?

Accepted Answer

Amplitude $$A = 0.10\ \mathrm{m}$$, frequency $$f = 5\ \mathrm{Hz}$$

Question 11

A $$9\ \mathrm{V}$$ battery is connected to a $$3\ \Omega$$ resistor. What is the current through the resistor?

Accepted Answer

$$I = \frac{V}{R} = 3\ \mathrm{A}$$

Question 12

A sound source emits a power of $$2.0\ \mathrm{W}. At $$what distance from the source is the intensity $$0.02\ \mathrm{W/m^2$}$$?

Accepted Answer

$$r = \sqrt{\frac{P}{4\pi I}} = 2.82\ \mathrm{m}$$

Question 13

A $$0.2\ \mathrm{kg}$$ mass oscillates on a spring with $$k = 50\ \mathrm{N/m}. $$What is the angular frequency $$\omega$$?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}} = 15.8\ \mathrm{rad/s}$$

Question 14

A $$10\ \Omega$$ resistor dissipates $$20\ \mathrm{W} of $$power. What is the voltage across it?

Accepted Answer

$$V = \sqrt{P R} = 14.1\ \mathrm{V}$$

Question 15

A string has a linear density $$\mu = 0.01\ \mathrm{kg/m}$$ and is under a tension of $$100\ \mathrm{N}. $$What is the speed of a wave on the string?

Accepted Answer

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

Question 16

A sound has an intensity of $$1.0 	imes 10$$^{-6}$$\ \mathrm{W/m^2$}. $$What is its sound level in decibels?

Accepted Answer

$$\beta = 10 \log_{10}\left(\frac{I}{I_0$}\right) = 60\ \mathrm{dB}$$

Question 17

A $$5\ \Omega$$ and a $$15\ \Omega$$ resistor are connected in parallel. What is the total current if a $$10\ \mathrm{V}$$ battery is connected across them?

Accepted Answer

$$I_{total} = \frac{V}{R_{eq}} = 2.5\ \mathrm{A}$$

Question 18

A mass on a spring has total mechanical energy $$E = \frac{1}{2}kA^2$. At x$$ = \frac{A}{2}$$, what is the kinetic energy?

Accepted Answer

$$KE = \frac{3}{8}kA^2$

Question 19

A diatomic gas has $$\gamma = 1.4. If $$the speed of sound in the gas is $$v = 340\ \mathrm{m/s}$$ and the molar mass is $$0.028\ \mathrm{kg/mol}$$, what is the temperature of the gas? (Use $$R = 8.31\ \mathrm{J/(mol\cdot K)})$$

Accepted Answer

$$T = \frac{v^2$ M}{\gamma R} = 3,140\ \mathrm{K}$$

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