Physics 102
Homework Set 6
Solutions

Chapter 19:
Exercises: 

4) A swing is an example of a pendulum.  When you stand up on a swing,
   you are effectively shortening the length of the pendulum (since
   the distance from the axis of the pendulum to the center of mass is
   less).  If you shorten a pendulum, you decrease its period.

   You can also think about this from the standpoint of rotational
   inertia.  When you stand up, you get closer to the axis of
   rotation, decreasing the rotational inertia.  This allows the swing
   to go back and forth in a shorter period of time.

24) When you halve the wavelength, the frequency must double (since
    the velocity is unchanged).  v = lambda * f.

    A violinist can use this technique to double the pitch of the
    note she is playing, effectively raising it by one octave.

26) a) When the locomotive is coming toward you, you hear the frequency of
    the whistle increase because of the Doppler shift.  b) the
    wavelength also decreases (you can see this in figure 19.16 where
    the wave crests are closer together approaching point B).  c) the
    velocity of sound in air is unchanged.  The air does not care how
    the high pitched sound is made (whether it is made by a high
    pitched whistle at rest or by a low pitched whistle moving toward
    you).  The speed of sound in air is determined by the thermal
    velocity of the air molecules.  This is not changed by the motion
    of the locomotive.

    Note that this is a completely different case from one where you
    throw a ball from the locomotive.  In that case, the velocity
    of the ball is increased by throwing it from the locomotive (if
    you throw it forwards).  For throwing a ball, the velocities add
    up.  For a sound wave, the velocity does not change, but the
    frequency and wavelength change instead.

30) This means that the light coming to us from one edge of the sun is
    bluer and the light coming to us from the other edge is redder.
    This means that the one edge is moving toward us and the other
    edge is moving away from us.  This means that the sun is spinning
    (rotating). 

34) The shock wave angle narrows as the plane increases its speed.
    See figure 19.20 for an example.  This is also true for motorboats
    and jetskis.  Look at the wake the next time you go boating and
    notice its opening angle as you vary the speed of the boat.  BTW:
    an acceptable reason for this answer is: 'I saw it while I was
    boating.' 

Problems: 

4) The frequency f is 2 Hz or 2 (1/s) since it makes two cycles every
   second.  The period T is 0.5 s since it takes 1/2 second for each
   cycle.  In one cycle, the weight goes from bottom, through the
   average position, to the top, and back down again.  Remember that
   the amplitude is the distance from the average position to the
   maximum (or to the minimum).  Since it is a distance of 20 cm from
   min to avg to max to avg to min, it is a distance of 5 cm from
   average to maximum.  Thus the amplitude is 5 cm.

6) v = lambda * f so that lambda = v / f = 340 m/s / 600 1/s = 0.57 m

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Chapter 20:

Exercises:

4) 101.1 on the FM dial means that it the radio station is
   broadcasting at 101.1 MHz = 1.011 * 10^8 Hz.	

6) The electromagnetic wave travels MUCH faster.  The same frequency
   means that  the time between wave crests is the same.  In that same
   time, the electromagnetic wave travels much farther, therefore its
   wavelength is much bigger.

   We can do the same thing by equation:  lambda = v / f.  If v is
   much bigger, then lambda will be much bigger.

8) Olympic track races are frequently decided by differences of 0.01
   second or less.  If there are ten runners and each runner is
   separated by a distance of 1.5 m, then there is a distance of
   almost 15 m between the runners closest to and farthest from the
   starting gun.  The time it takes sound to travel that far is 
   time = distance / velocity = 15 m / 340 m/s = 0.05 s
   (approximately).  This gives an unfair advantage to the closest
   runner.  

   When the sound is picked up by a microphone, it is transmitted
   electrically at almost the  speed of light to the speakers near
   each starting block.  This reduces the time lag to nanoseconds
   (billionths of a second) and makes it irrelevant.