Question

# 2 Amplitude Modulation When two musical notes are nearly the same pitch, one can hear “beats”...

2 Amplitude Modulation
When two musical notes are nearly the same pitch, one can hear “beats” — a periodic rise and fall in the volume of a single pitch.

(a) Generate a plot of this phenomenon. Create — and upload — a graph of the waveform f(t) that results from superposition of two waves with similar frequencies:

f1(t) =cos21t, f2(t) =cos19t, f(t) = f1(t)+f2(t)

(b) Describe the significant features of your plot. What pitch would you hear? At what frequency does the volume oscillate?

In AM radio, a high-frequency carrier wave is combined with a low-frequency signal wave. The waves are not simply added together. Rather, the low frequency wave is used to modulate the amplitude of the high frequency wave.
(c) Create — and upload — a graph of the waveform f(t) that illustrates this idea: f(t) = (1 + 0.4cos2t)*cos20t

(d) Describe the significant features of your plot. In what ways is it similar to the plot from part (a)? In what ways is it different?

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