An interesting phenomenon in the generation of musical sounds is beating or pulsation. Suppose NP different players try to play a pure tone, a sinusoid of frequency 160 Hz, and that the signal recorded is the sum of these sinusoids. Assume the NP players while trying to play the pure tone end up playing tones separated by ­ˆ†Hz, so that the recorded signal is

where the f_i are frequencies from 159 to 161 separated by ­ˆ† Hz. Each player playing a different frequency.

(a) Generate the signal y(t) 0 ‰¤ t ‰¤ 200 (sec) in MATLAB. Let each musician play a unique frequency. Consider an increasing number of players, letting NP to go from 51 players, with ˆ† ­= 0.04 Hz, to 101 players with ˆ† ­= 0.02 Hz. Plot y(t) for each of the different number of players.

(b) Explain how this is related with multi-path and the Doppler effect discussed in the previous problems.

Transcribed Image Text:

NP γit) 10 cos (2π/ft) γt) i=1