Q: A sound wave travels through air at 20°C. What is its speed?

$$v = 331 + 0.6T = 331 + 0.6 \times 20 = 343\ \mathrm{m/s}$$

Q: A 0.5 m long organ pipe is open at both ends. What is the wavelength of the fundamental standing wave?

$$\lambda = 2L = 2 \times 0.5 = 1.0\ \mathrm{m}$$

Q: A sound wave has an intensity of $$5.5 \times 10$$^{-6}$$\ \mathrm{W/m^2$}. $$What is its sound level in decibels (dB)? Use $$I_0 = 1.0$$ \times $$10^{-12}$$\ \mathrm{$$W/m^2$$}$$.

$$\beta = 10 \log_{10} \left( \frac{I}{I_0$} \right ) = 10 \log_{10} \left( \frac{5.5 \times 10$$^{-6}$$}{1.0 \times 10$$^{-12}$$} \right ) = 67\ \mathrm{dB}$$

Q: Two point charges, $$q_1 = +2$$\ \mu\mathrm{C}$$ and q_2$ = -3\ \mu\mathrm{C}$$, are separated by 0.5 m. What is the magnitude of the force between them? ($$k = 8.99 \times 10^9$\ \mathrm{Nm^2$/C^2$$}$)

$$F = k \frac{|q_1$ q_2$|}{r^2$} = 8.99 \times 10^9$ \frac{2 \times 10$$^{-6}$$ \times 3 \times 10$$^{-6}$$}{(0.5)^2$} = 0.216\ \mathrm{N}$$

Q: A proton is placed in a uniform electric field of $$E = 1.0 \times 10^4$\ \mathrm{N/C}. $$What is the magnitude of the force acting on the proton?

$$F = qE = 1.6 \times 10$$^{-19}$$ \times 1.0 \times 10^4$ = 1.6 \times 10$$^{-15}$$\ \mathrm{N}$$

Q: An electron is accelerated from rest through a potential difference of 100 V. What is its final kinetic energy?

$$K = qV = 1.6 \times 10$$^{-19}$$ \times 100 = 1.6 \times 10$$^{-17}$$\ \mathrm{J}$$

Question 1

A string of length 2.0 m is fixed at both ends and vibrates in its fundamental mode. If the speed of the wave on the string is 120 m/s, what is the frequency of the fundamental mode?

Accepted Answer

$$f = \frac{v}{L} = \frac{120}{2} = 60\ \mathrm{Hz}$$

Question 2

Which of the following statements correctly describes the difference between transverse and longitudinal waves?

Accepted Answer

In transverse waves, particle motion is perpendicular to wave propagation; in longitudinal waves, it is parallel.

Question 3

A sound wave travels through air at 20°C. What is its speed?

Accepted Answer

$$v = 331 + 0.6T = 331 + 0.6 	imes 20 = 343\ \mathrm{m/s}$$

Question 4

A 0.5 m long organ pipe is open at both ends. What is the wavelength of the fundamental standing wave?

Accepted Answer

$$\lambda = 2L = 2 	imes 0.5 = 1.0\ \mathrm{m}$$

Question 5

A sound wave has an intensity of $$5.5 	imes 10$$^{-6}$$\ \mathrm{W/m^2$}. $$What is its sound level in decibels (dB)? Use $$I_0 = 1.0$$ 	imes $$10^{-12}$$\ \mathrm{$$W/m^2$$}$$.

Accepted Answer

$$\beta = 10 \log_{10} \left( \frac{I}{I_0$} ight ) = 10 \log_{10} \left( \frac{5.5 	imes 10$$^{-6}$$}{1.0 	imes 10$$^{-12}$$} ight ) = 67\ \mathrm{dB}$$

Question 6

A train approaches a stationary observer at a speed of 30 m/s. If the train's whistle emits a frequency of 500 Hz and the speed of sound is 340 m/s, what frequency does the observer hear?

Accepted Answer

$$f' = f \frac{v}{v - v_s} = 500 \frac{340}{340 - 30} = 500 \frac{340}{310} \approx 548\ \mathrm{Hz}$$

Question 7

Which of the following best describes the conservation of electric charge?

Accepted Answer

Electric charge is always conserved in an isolated system.

Question 8

Two point charges, $$q_1 = +2$$\ \mu\mathrm{C}$$ and q_2$ = -3\ \mu\mathrm{C}$$, are separated by 0.5 m. What is the magnitude of the force between them? ($$k = 8.99 	imes 10^9$\ \mathrm{Nm^2$/C^2$$}$)

Accepted Answer

$$F = k \frac{|q_1$ q_2$|}{r^2$} = 8.99 	imes 10^9$ \frac{2 	imes 10$$^{-6}$$ 	imes 3 	imes 10$$^{-6}$$}{(0.5)^2$} = 0.216\ \mathrm{N}$$

Question 9

A proton is placed in a uniform electric field of $$E = 1.0 	imes 10^4$\ \mathrm{N/C}. $$What is the magnitude of the force acting on the proton?

Accepted Answer

$$F = qE = 1.6 	imes 10$$^{-19}$$ 	imes 1.0 	imes 10^4$ = 1.6 	imes 10$$^{-15}$$\ \mathrm{N}$$

Question 10

Which of the following materials is a good electrical conductor?

Accepted Answer

Copper

Question 11

An electron is accelerated from rest through a potential difference of 100 V. What is its final kinetic energy?

Accepted Answer

$$K = qV = 1.6 	imes 10$$^{-19}$$ 	imes 100 = 1.6 	imes 10$$^{-17}$$\ \mathrm{J}$$

Question 12

A spherical sound wave radiates outward from a point source. If the power output is 10 W, what is the intensity at a distance of 2 m?

Accepted Answer

$$I = \frac{P}{4\pi r^2$} = \frac{10}{4\pi (2)^2$} = \frac{10}{16\pi} \approx 0.20\ \mathrm{W/m^2$}$$

Question 13

A tube closed at one end and open at the other has a length of 0.75 m. What is the wavelength of its fundamental mode?

Accepted Answer

$$\lambda = 4L = 4 	imes 0.75 = 3.0\ \mathrm{m}$$

Question 14

A charged particle of mass $$m$$ and charge $$q is $$placed in a uniform electric field $$E. $$What is its acceleration?

Accepted Answer

$$a = \frac{qE}{m}$$

Question 15

Which of the following best describes the relationship between electric field and electric potential in a uniform field?

Accepted Answer

$$E = -\frac{\Delta V}{d}$$

Question 16

A sound-insulating door reduces the sound level by 40 dB. What fraction of the original sound intensity passes through the door?

Accepted Answer

$$\frac{I}{I_0$} = 10$$^{-4}$$

Question 17

Which of the following is true about electric field lines?

Accepted Answer

Electric field lines start on positive charges and end on negative charges.

Physics 103: Waves, Sound, and Electricity – Study Notes

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