Phys102 -- 9th Assignment

This homework is due at the beginning of lecture Tuesday, November 11.

41. Of the waves shown with problem 36 (assignment 8),

1. which wave can be obtained by low-pass filtering one of the basic wave shapes? Which wave shape?
2. which wave(s) can be obtained by modulating a sine wave? What kind of modulation?

42. Text, problem 5-1.

43. Text, problem 5-2 (just draw the waves, forget about indicating how you proceeded).

44. A car is repeatedly driving at constant speed around a circular race track, and emits a sound of constant frequency (as measured in the car). An observer some distance away hears a modulated sound, due both to the changing velocity of the car, and the changing distance of the car. Mention the two effects or laws from Chapter 2 responsible for the modulation. and draw (roughly) what the modulated wave might look like, starting at the moment when the car is closest to the observer (i.e. when the sound is loudest).

45. Text, problem 5-4

Solutions

1. wave 2 (from top). The filtering will round off the corners of the sawtooth wave. (Note that a real filter does not produce wave shapes like the "sum wave" in Fig 4-6)
2. wave 4 can be described as a sine wave balanced (amplitude) modulated by a sine wave.

42.

1.  
   1. gating: The sound is on (amplitude positive), the off (amplitude zero), then on (amplitude positive, etc.
   2. amplitude modulation: The sound gets louder (amplitude large), then softer (amplitude small), then louder, etc.
   3. frequency modulation: The pitch gets slightly higher (frequency higher), then slightly lower (frequency lower), then slightly higher (frequency higher), etc.
   4. balanced modulation: The same as amplitude modulation but with offset value zero. In general, a complex tone having non-integrally related components results, which can sound like a bell.
2. The carrier wave is typically the higher frequency wave; the modulator wave affects or otherwise controls some property of the carrier wave. For instance, in amplitude modulation, the modulator affects the amplitude of the carrier wave; in frequency modulation the modulator affects the frequency of the wave.
3. Amplitude modulation: tremulo. Frequency modulation: vibrato.

43.

44. The distance between car and observer changes periodically. Because of the inverse square law, the intensity and hence the amplitude of the wave changes (amplitude modulation), with a maximum when the car is closest to the observer. There is also a Doppler effect, changing the wave's observed frequency (frequency modulation), where the highest frequency occurs when the car is moving most rapidly toward the observer. So the FM is 90° out of phase with the AM. To draw this accurately is a bit of a challenge. Here is the corresponding question and picture from last year's exam:
The wave from a sinusoidal source that moves back and forth with respect to the observer appears both amplitude and frequency modulated. Of the two graphs shown below, only one can come from such a source. (Time is running from left to right, as usual.) To find out which, mark the following times on the graph with a letter as follows:

C: source closest to observer
A: source moving fastest away from observer
F: source farthest from observer
T: source moving fastest toward observer

You will note only one of the graphs allows consistent labeling. Cross out the other one with a big X.

45. Audio signals are in the range 0 to 20 kHz. Control signals (typically 0 to 30 Hz) control properties of the audio signal, including attack and decay times, vibrato frequency and amplitude, etc. The audio signal provides the pitch and timbre of the musical note.