Interference Homework

1. I set up two speakers in the classroom and play the same tone (i.e. they have the same frequency and wavelength) through both speakers. When Maria is standing 3 meters from one speaker and 4.5 meters from the other, she observes a loud spot.

(a) What are two possible wavelength of the sound coming out of the speakers that could account for this loud spot?

(b) If Maria maintains a distance of 3 meters from the first speaker, how far from the second speaker must she stand to experience a quiet spot? Give two possible distances.

2. A radio wave takes two paths to get from the transmitter to the receiver. One path goes in a straight line across, and the other bounces off the ground half way between the two radio towers, as depicted above. When the two radio waves meet at the receiver, they cancel out, producing destructive interference. If each tower has a height of h = 50 m, and they are separated by a distance of d = 120 m, what is one possible value for the wavelength of the radio waves.

3. The acoustical system shown in the figure below is driven by a speaker emitting a 520 Hz note. The sound from the speaker is split up along two paths that then rejoin when they reach your ear.

(a) If the speed of sound is 345 m/s, what is the wavelength of the sound emitted by the speaker.

(b) When the sound waves rejoin at your ear, they interfere constructive. If r1 = 0.25 m (the bottom path), what must r2 be equal to?

(c) If, on the other hand, when the sound waves rejoin at your ear, they are out-of-phase, what must r2 be equal to? (r1 still equals 0.25 meters.)

4. You are trying to tune your guitar to C, 512 Hz. When you pluck the string while a 512-Hz tuning fork resonates, you hear beats with a frequency of 4 Hz. What is the frequency of your vibrating guitar string?

5. Why is there a Doppler effect when the source of sound is stationary and the listener is in motion? In which direction should the listener move to hear a high frequency? a lower frequency? Explain.

6. A railroad locomotive is at rest with its whistle shrieking, then starts moving toward you.

a. Does the frequency that you hear increase, decrease, or stay the same? Explain.

b. How does the wavelength change? Explain.

c. How does the speed of sound change? Explain.

7. Astronomers find that light emitted by a particular element at one edge of the Sun has a slightly higher frequency than light from that element emitted at the opposite edge. What do these measurements tell us about the motion of the Sun? Explain.

8. If the frequency of the 5th Harmonic of a standing wave is 256 Hz, (a) What is the fundamental frequency? (b) What is the frequency of the 3rd Harmonic?

5. Two sources of radio waves of the same frequency and wavelength are located at points A and B along the shoreline (as depicted here). They are separated by a distance of x = 240 meters. When the ship is at point D, directly across from point B, a distance of y = 70 meters away, it is found that the radio waves are out of phase, thus producing a minimum.

What is one possible wavelength that the radio waves could have to produce this minimum?