P105 Homework Assignment #4: Waves & Sound, Wave Properties II | Complete Solution

Physics P105:
Homework Assignment #4:

Waves & Sound, Wave Properties II

Make sure you show your work online where relevant.

1. When incident and reflected waves overlap, interference may be (leading to a large wave motion) or (leading to a smaller wave motion).
2. If the diameter of a trumpet bell is about 10 cm, the sound wave from the trumpet (a or b) , where (a) emerges in a narrow beam or (b) spreads out in all directions. Assume it is playing a note with a frequency of 1000 Hz (justify your answer, and use vsound = 343 m/s).

3. When there is a temperature inversion, the temperature close to the ground is , and the temperature higher up is . As a result, the speed of sound close to the ground is than the speed higher up, and the sound wave is refracted or bent back towards the ground.

4. When a sound source, such as a supersonic plane, moves faster than the speed of sound, a cone-shaped (two words) is produced, creating a (two words) as it passes stationary observers.

5. A small "tweeter" has a diameter of 5.0 cm. Diffraction effects from the tweeter are important for frequencies below approximately Hz.

6. To "see" some object using ultrasound, it is necessary to avoid diffraction by using ultrasonic sound waves with a wavelength smaller than the object being viewed. To be able to resolve features on a fetus of size less than 1.0 mm, the frequency of the ultrasound needs to be greater than kHz.

7. You stand 300 m away from a cliff and loudly yell "yop". How long does it take for you to hear the echo? s. (assume speed of sound is 343 m/s).

8. Two waves of the same frequency have amplitudes A and 2A. In traversing the same medium, they undergo interference. If the interference is constructive, then the amplitude is A. If the interference is destructive, then the amplitude is A.

9. You know a car's horn when the car is stationary has a frequency of 660 Hz. It is towards you and you measure a sound frequency of 600 Hz. How fast is the car moving towards you?

10. Two identical loudspeakers emitting the same pure tones (f = 343 Hz) are facing each other at a distance of L = 10.0 m. If the speed of sound is 343 m/s, the wavelength λ = m. An observer positioned in the middle between the two speakers and so an equal distance from each speaker hears (constructive/destructive) interference. It can be changed to (constructive/destructive) interference by moving m towards one of the speakers.
Center
S1 S2
Δx
L
d1 d2

11. A tuning fork of frequency 256 Hz is used to tune a piano. When the tuning fork is played at the same
time as the piano, a beat frequency of 3 Hz is heard. What are the possible frequencies of the piano?
12. A string fixed at both ends has a length L = 75 cm. The wavelengths of the fundamental and of the
next two harmonics are;
λ1 = __________ m, λ2 = __________ m, λ3 = __________ m.
13. A string fixed at both ends has a length L = 75 cm. If the velocity of transverse waves on this string is
125 m/s, the fundamental frequency f1 = ____________ Hz.
14. A nylon guitar string, 65 cm long, has a mass of 5.8 x 10-4 kg and a tension of 54 N. The frequencies of
the 3 lowest resonance modes are , , and Hz.
15. A certain string is found to have a frequency difference between the 3rd and 5th harmonic of
250 Hz. The frequency of the fundamental mode f1 = ____________ Hz.
Tear off and hand in at the start of lecture on Wednesday, Feb. 11
Name: ID
15. (6 pts) Draw and add together the following pairs of waves:
(a) square waves of equal amplitudes with frequencies f (already drawn for you below) and 2f, beginning in
phase:
time
1 frequency f
0
-1
-2
2
(b) similar waves, but beginning 180 degrees out of phase:
time
1 frequency f
0
-1
-2
2