Sound and Wave problems

1. Consider a string vibrating on a guitar at 320 Hz (E note). If the string length is 0.6-m, find the following:

a. wavelength of first 3 harmonics

b. frequency of first 3 harmonics

c. speed of first 3 harmonics

2. Now imagine an organ pipe, open on both ends. The speed of sound is 340 m/s. Find the following:

a. length of tube needed to create a resonant frequency of 150 Hz.

b. frequencies and wavelengths of first 3 harmonics

c. wave shapes of first 3 harmonics

d. the effect of capping the tube at one end

3. Most instruments in western music are tuned to a 440 Hz (A) standard. That is, the note middle A is defined as 440 Hz. Find the following frequencies:

a. one octave below

b. two octaves below

c. 1 semi-tone (piano key) above

d. 3 semi-tones above

4. (In advance of next class) Consider a police car, traveling at 35 m/s, with a siren at 1000 Hz. Find the frequencies when the car does the following:

a. approaches you (with you at rest)

b. passes you (with you at rest)

c. approaches you (with you traveling toward the car at 15 m/s)

d. passes you (with you traveling away from the car at 15 m/s)

5. Distinguish between mechanical and electromagnetic waves, giving examples.

6. Distinguish between transverse and longitudinal waves, giving examples.

7. What is the frequency of a 120 x 10^-11 m X-ray?