Conceptual Questions:
1. Why did I say that the spring "compressional" wave is really a transverse wave?
2. Describe at least one transverse wave and one longitudinal wave NOT mentioned in the book or in lecture.
3. What phenomenon is created by two tuning forks, side by side, emitting frequencies which differ by only a small amount?
a. resonance
b. interference
c. the Doppler effect
d. beats
Numerical Problems: answers link to a help page.
1. A long string is pulled so that the tension in it increases by a factor of three. By what factor does the wave velocity change?
2. If the frequency of a traveling wave train is increased by a factor of three in a medium where the velocity is constant, which of the following is the result?
a. The amplitude is one third as big.
b. The amplitude is tripled.
c. The wavelength is one third as big.
d. The wavelength is tripled.
3. What is the phase difference when two waves, traveling in the same medium, undergo constructive interference?
4. A traveling wave train has wavelength 0.50 m, speed 20 m/s. Find the wave frequency.
5. A musical tone, sounded on a piano, has a frequency of 410 Hz and a wavelength in air of 0.80 m. What is the wavespeed?
6. Tripling the density, in mass per unit length, of a guitar string will result in changing the wave velocity in the string by what factor?
7. If a wave pulse is reflected from a free boundary, which of the following choices best describes what happens to the reflected pulse?
a. It becomes inverted.
b. It remains upright.
c. It is halved in amplitude.
d. It is doubled in amplitude.
8. As a gust of wind blows across a field of grain, a wave can be seen to move across the field as the tops of the plants sway back and forth. This wave is a
a. transverse wave.
b. longitudinal wave.
c. polarized wave.
d. interference of waves.
9. Consider two identical wave pulses on a string. Suppose the first pulse reaches the fixed end of the string and is reflected back and then meets the second pulse. When the two pulses overlap exactly, the superposition principle predicts that the displacement of the resultant pulses, at that moment, will be what factor times the amplitude of one of the original pulses?
10. Bats can detect small objects such as insects that are of a size approximately that of one wavelength. If bats emit a chirp at a frequency of 60 kHz, and the speed of sound waves in air is 330 m/s, what is the smallest size insect they can detect?
11. A 2-m long piano string of mass 10 grams is under a tension of 338 N. Find the velocity with which a wave travels on this string.
ans: 260 m/s 12. Two vibrating tuning forks, held side by side, will create a beat frequency of what value if the individual frequencies of the two forks are 342 Hz and 345 Hz, respectively?