Three equal-amplitude tones of frequencies 499 Hz, 500 Hz and 501 Hz are started in phase. Their resultant can be written in the form A[1+2cos(2πNt)]cos(2π500t). Find N.
Physics · Wave Motion · beat and properties of sound
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Question

Three equal-amplitude tones of frequencies 499 Hz, 500 Hz and 501 Hz are started in phase. Their resultant can be written in the form A[1+2cos(2πNt)]cos(2π500t). Find N.

G1 Physics · Accepted Answer

Add the 499 Hz and 501 Hz terms: cos(2π499t)+cos(2π501t) = 2cos(2πt)cos(2π500t). Including the 500 Hz tone, y = A[1+2cos(2πt)]cos(2π500t). Comparing with A[1+2cos(2πNt)]cos(2π500t), we get N = 1.