Q: What is the intensity level in decibels of a sound wave with intensity $$4.37 \times 10$$^{-7}$$\ \mathrm{W/m^2$}$$?

$$\beta = 10 \log_{10} \left( \frac{I}{I_0$} \right) = 10 \log_{10} \left( \frac{4.37 \times 10$$^{-7}$$}{1.0 \times 10$$^{-12}$$} \right) = 56.4\ \mathrm{dB}$$

Q: If the intensity of a certain sound wave is $$2 \times 10^7$\ \mathrm{W/m^2$}$$, and its intensity is raised by 30 decibels, what is the new intensity in $$\mathrm{W/m^2$}$$?

$$I_2$$ = $$I_1$$ \times $$10^{\frac{\Delta \beta}$${10}} = 2 \times $$10^7$$ \times $$10^{3} = 2$$ \times $$10^{10}$$\ \mathrm{$$W/m^2$$}$$

Q: A 500-Hz whistle is moved toward a listener at a speed of 10.0 m/s. At the same time, the listener moves at a speed of 20.0 m/s in a direction away from the whistle. What is the apparent frequency heard by the listener? (Speed of sound is 340 m/s.)

$$f' = f \frac{v + v_{\text{listener}}}{v - v_{\text{source}}} = 500 \frac{340 + 20}{340 - 10} = 485\ \mathrm{Hz}$$

Q: The attractive electrostatic force between two point charges $$4 \times 10$$^{-6}$$\ \mathrm{C}$$ and Q has a magnitude of 1.77 N when the separation between charges is 25 cm. The sign and magnitude of the charge Q is closest to:

$$Q = \frac{F r^2$}{k q_1$} = \frac{1.77 \times 0.25^2$}{8.99 \times 10^9$ \times 4 \times 10$$^{-6}$$} = 3 \times 10$$^{-6}$$\ \mathrm{C}$$, negative

Q: A 2 mg particle carrying a charge of $$4 \mu\mathrm{C} is $$placed in a uniform electric field of magnitude of 100 N/C. Find the particle's acceleration.

$$a = \frac{qE}{m} = \frac{4 \times 10$$^{-6}$$ \times 100}{2 \times 10$$^{-6}$$} = 0.2\ \mathrm{m/s^2$}$$

Q: How many electrons are removed from a metal ball if the ball is to carry a positive charge of $$3.2\ \mathrm{nC}$$? $$(e = 1.6 \times 10$$^{-19}$$\ \mathrm{C})$$

$$n = \frac{Q}{e} = \frac{3.2 \times 10$$^{-9}$$}{1.6 \times 10$$^{-19}$$} = 2 \times 10$$^{10}$$

Question 1

A sinusoidal wave of length 1.2 m travels along a string. If the period of the wave is 0.48 s, what is the wave speed in m/s?

Accepted Answer

$$v = \frac{\lambda}{T} = \frac{1.2}{0.48} = 2.5\ \mathrm{m/s}$$

Question 2

A rope with a total mass of 25.0 kg is tied to a tree on one side of a 125-m wide ravine. You are pulling on the other end of the rope with a force of 415 N. If you pluck the rope at your end, how long will it take the pulse to travel across the ravine to the tree?

Accepted Answer

$$t = \frac{d}{v} = \frac{125}{45.5} = 2.74\ \mathrm{s}$$

Question 3

A string of linear mass of $$0.0015\ \mathrm{kg/m} is $$under a tension of 40 N. What should its length be if the frequency of the second harmonic is 440 Hz?

Accepted Answer

$$L = \frac{v}{2f} = \frac{\sqrt{\frac{F}{\mu}}}{2f} = \frac{\sqrt{\frac{40}{0.0015}}}{2 	imes 440} = 0.26\ \mathrm{m}$$

Question 4

A standing wave is set up on a 180 g string, 6 m long as shown. What is the frequency of the wave if the string is under tension of 120 N?

Accepted Answer

$$f = 129\ \mathrm{Hz}$$

Question 5

What is the intensity level in decibels of a sound wave with intensity $$4.37 	imes 10$$^{-7}$$\ \mathrm{W/m^2$}$$?

Accepted Answer

$$\beta = 10 \log_{10} \left( \frac{I}{I_0$} ight) = 10 \log_{10} \left( \frac{4.37 	imes 10$$^{-7}$$}{1.0 	imes 10$$^{-12}$$} ight) = 56.4\ \mathrm{dB}$$

Question 6

If the intensity of a certain sound wave is $$2 	imes 10^7$\ \mathrm{W/m^2$}$$, and its intensity is raised by 30 decibels, what is the new intensity in $$\mathrm{W/m^2$}$$?

Accepted Answer

$$I_2$$ = $$I_1$$ 	imes $$10^{\frac{\Delta \beta}$${10}} = 2 	imes $$10^7$$ 	imes $$10^{3} = 2$$ 	imes $$10^{10}$$\ \mathrm{$$W/m^2$$}$$

Question 7

A 500-Hz whistle is moved toward a listener at a speed of 10.0 m/s. At the same time, the listener moves at a speed of 20.0 m/s in a direction away from the whistle. What is the apparent frequency heard by the listener? (Speed of sound is 340 m/s.)

Accepted Answer

$$f' = f \frac{v + v_{	ext{listener}}}{v - v_{	ext{source}}} = 500 \frac{340 + 20}{340 - 10} = 485\ \mathrm{Hz}$$

Question 8

An organ pipe, open at both ends, is 2.22 m long. If the velocity of sound in air is 343 m/s, the frequency of the third harmonic of this pipe is:

Accepted Answer

$$f = 234\ \mathrm{Hz}$$

Question 9

The attractive electrostatic force between two point charges $$4 	imes 10$$^{-6}$$\ \mathrm{C}$$ and Q has a magnitude of 1.77 N when the separation between charges is 25 cm. The sign and magnitude of the charge Q is closest to:

Accepted Answer

$$Q = \frac{F r^2$}{k q_1$} = \frac{1.77 	imes 0.25^2$}{8.99 	imes 10^9$ 	imes 4 	imes 10$$^{-6}$$} = 3 	imes 10$$^{-6}$$\ \mathrm{C}$$, negative

Question 10

A 2 mg particle carrying a charge of $$4 \mu\mathrm{C} is $$placed in a uniform electric field of magnitude of 100 N/C. Find the particle's acceleration.

Accepted Answer

$$a = \frac{qE}{m} = \frac{4 	imes 10$$^{-6}$$ 	imes 100}{2 	imes 10$$^{-6}$$} = 0.2\ \mathrm{m/s^2$}$$

Question 11

How many electrons are removed from a metal ball if the ball is to carry a positive charge of $$3.2\ \mathrm{nC}$$? $$(e = 1.6 	imes 10$$^{-19}$$\ \mathrm{C})$$

Accepted Answer

$$n = \frac{Q}{e} = \frac{3.2 	imes 10$$^{-9}$$}{1.6 	imes 10$$^{-19}$$} = 2 	imes 10$$^{10}$$

Question 12

Two stationary point charges $$q_1$$ and $$q_2$$ are shown in the figure along with a sketch of some field lines representing the electric field produced by them. What can you deduce from the sketch?

Accepted Answer

q1 is negative and q2 is positive; the magnitude of q1 is less than the magnitude of q2.

Question 13

Determine the magnitude and direction of the electric field midway between a $$-8\mathrm{nC}$$ and a $$-6\mathrm{nC}$$ charge 60 cm apart.

Accepted Answer

$$E = \frac{k|q_1$|}{r^2$} - \frac{k|q_2$|}{r^2$} = 200\ \mathrm{N/C} to $$the left

Question 14

What is the speed of a proton that has been accelerated from rest through a potential difference of 4.0 kV? $$(m_p = 1.67 	imes 10$$^{-27}$$\ \mathrm{kg}, e = 1.6 	imes 10$$^{-19}$$\ \mathrm{C})$$

Accepted Answer

$$v = \sqrt{\frac{2qV}{m}} = \sqrt{\frac{2 	imes 1.6 	imes 10$$^{-19}$$ 	imes 4000}{1.67 	imes 10$$^{-27}$$}} = 8.8 	imes 10^5$\ \mathrm{m/s}$$

Question 15

How strong is the electric field between two parallel plates 8 cm apart if the potential difference between them is 50 V?

Accepted Answer

$$E = \frac{\Delta V}{d} = \frac{50}{0.08} = 625\ \mathrm{V/m}$$

Question 16

A pipe closed at one end has a length of 1.5 m. If the speed of sound in air is 343 m/s, what is the frequency of the second harmonic?

Accepted Answer

$$f_n = n \frac{v}{4L}, n = 3: f_3$ = 3 \frac{343}{4 	imes 1.5} = 171\ \mathrm{Hz}$$

Question 17

A 0.2 kg mass is attached to a string and swung in a horizontal circle of radius 0.5 m at a speed of 2 m/s. What is the tension in the string?

Accepted Answer

$$T = \frac{mv^2$}{r} = \frac{0.2 	imes 2^2$}{0.5} = 1.6\ \mathrm{N}$$

Question 18

A sound wave has a frequency of 1000 Hz and a wavelength of 0.34 m. What is the speed of sound in the medium?

Accepted Answer

$$v = f \lambda = 1000 	imes 0.34 = 340\ \mathrm{m/s}$$

Waves, Sound, and Electric Fields: Physics Study Guide with Worked Examples

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