Physics 150 Fall 2003
Solution to HW 5
1. You should write
a short description containing the main points: In classical physics waves show
interference; particles have mass and obey
2. Electric force in
FC = 9.0 x 109 (Nm2/C2) (0.002 C)2 / (0.5m)2 = 1.44 x 105 N
Gravitational force in
FC = 6.66 x 10-11 (Nm2/Kg2) (1000 Kg)2 / (0.5m)2 = 2.66 x 10-4 N
3. Question A, Ch. 7 of March: There can be many examples: water waves, waves in the earth due to an earthquake, tidal waves, waves in water due to the sound of a whale, waves on a drum head, waves on a speaker cone, ……
4. Question C, Ch. 7 of March: The length the part of the string that vibrates is changed by the fingers. A change of one octave is accomplished by shortening the vibrating part of the string to ˝ its length.
5. Question D, Ch. 7 of March: The key point is that is the towers are ˝ wavelength apart, then if they broadcast identical signals, the waves are ˝ wavelength out of phase along a line that passes through the antennae. In those directions, the waves interfere destructively and the signal received by a radio is minimum. On a line perpendicular to the antennae the two waves add constructively and the signal is maximum.
6. Exercise 2, Ch. 7 of March: Since the speed of sound is 340 m/s, we can use v = 340 m/s = wavelength x frequency. Thus wavelength = 340 (m/s) / frequency, so that:
frequency = 20 Hz = 20 /s means wavelength = 17 m
frequency = 17,000 Hz = 20 /s means wavelength = 0.02 m
7. This is the same as above except the speed is c = 3 x 108 m/s. Thus:
Waves from WILL-AM which broadcasts at a frequency of 580 Khz = 580,000/s
have wavelength = c/ 580,000/s = 517 m = .517 Km
Waves from WILL-FM which broadcasts at a frequency of 90.9 Mhz = 90.9 x 106/s
have wavelength = c/ 90.9 x 106/s = 3.3 m
8. This is our everyday experience. We all set our clocks and assume everyone agrees. Even without “clocks” we do not observe time flowing differently for moving objects; for example, we do not see that airplane pilots age less than their “twins” on earth. With our everyday clocks and observations I think I could check accuracy to a few seconds a year (inexpensive modern watches are very accurate) and I could compare different clocks that have moved differently.
9. If v = 1.5 x 108 m/s, then v/c = 0.5 and gamma = 1/sqrt(1- 0.25) = 1/sqrt(0.75) = 1.1547
If v = 1.5 x 106 m/s, then v/c = 0.5 x 10-2 and gamma = 1/sqrt(1- 0.25 x 10-4) = 1.0000125