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

F_{C} = 9.0 x 10^{9} (Nm^{2}/C^{2}) (0.002 C)^{2}
/ (0.5m)^{2} = 1.44 x 10^{5} N

Gravitational force in

F_{C} = 6.66 x 10^{-11} (Nm^{2}/Kg^{2}) (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 10^{8} 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 10^{6}/s

have wavelength = c/ 90.9 x 10^{6}/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 10^{8}
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 10^{6}
m/s, then v/c = 0.5 x 10^{-2} and gamma = 1/sqrt(1-
0.25 x 10^{-4}) = 1.0000125