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 Newton’s equations

2.  Electric force in Newtons between two objects with charge 0.002 C spaced a distance 0.5 m apart.

FC =  9.0 x 109  (Nm2/C2) (0.002 C)2 / (0.5m)2 =  1.44 x 105  N

Gravitational force in Newtons between the same two objects if each has mass 1000 Kg:

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 ½ its length.

5.  Question D, Ch. 7 of March: The key point is that is the towers are ½ wavelength apart, then if they broadcast identical signals, the waves are ½ 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