S302, Kewley-Port 10/29/07

Homework 10 - All
Inverse Square Law, Beats and Standing Waves

1a. If a sound level is 65 dB at a distance of 50m from the source, what
is the dB at a distance of 100 m from the source?

a. 71 dB
b. 62 dB
c. 59 dB
d. 68 dB

1b. What is the level at 200 m from the source?

 

 

2. If a sound intensity level is 60 dB at 400 m, by how much will the
level be increased/decreased at a distance of 40 m?

 

 

 3. Two tones are playing with f1 = 400 Hz and f2 = 406Hz.
a) Describe the sound you will hear.

 

b) What is the beat frequency? What is the beat period?

 

c ) What is the frequency of the sound you hear?

 

d) Draw a waveform of this sound, labeling the time axis carefully.

 

 

 

 

e) If f2 is changed to 600 Hz, describe the nature of the resulting f1 + f2 sound.

 

 

4. There are two tones playing with a beat frequency of 5 Hz. f1 has the frequency of 50 Hz.
a) What is the frequency for f2?

 

b) What is the beat period?

 

 

c) To what frequency does this pitch sound?

 

5. Explain the concepts of a point source in an unbounded medium, the resulting spherical wave, and how these relate to a plane wave front.

 

6. Explain what a whispering gallery is and how it works.

 

 

7. a) Consider the transverse standing wave on a guitar string, L = .85 m. Draw the string in the 4th mode of vibration. Label all the nodes and antinodes.

 

 

 

b) The speed of sound on the string is 420 m/s. What is f0? What are the frequencies of the next 3 modes of vibration?

 

 

c) What is the wavelength on the string for first mode of vibration? For the 4th mode of vibration?

 

 

d) Explain what is happening to displacement and energy at the nodes at the ends of the guitar string?

 

 

8. How many 1/2 wavelengths are there in the 6th harmonic of a vibrating string? How many nodes are there?

 

 

9. a) Consider a longitudinal standing wave in an open-closed tube, L =  15 cm (the average length of a female vocal tract). Draw a standing wave in the tube in the 2nd mode of vibration. Label all the nodes and antinodes.

 

 

 

b) The speed of sound in air is 320 m/s. What is f0? What are the frequencies of the first three modes of vibration, F1, F2 and F3?

 

 

c) What is the wavelength for first mode of vibration? For the 2nd mode of vibration?

 

 

d) Explain what is happening to displacement and energy at the open end of the tube?

 

 

10. How many 1/4 wavelengths are there in the 3d mode of vibration in an open-close tube? How many nodes are there? What harmonic of the fundamental is this?