Two waves, travelling along the same direction, are given by
y1(x, t) = asin (w1t − k1x)
and y2 (x, t) = asin (w2t − k2x)
Suppose that the values of w1 and k1 are respectively slightly greater than w2 and
k2 . i) Obtain an expression for the resultant wave due to their superposition. ii)
Explain the formation of wave packet
1
Expert's answer
2018-03-13T11:09:07-0400
Superposition of two waves given by, y = y_1+y_2 …………………………(1) Put the values of y_1 and y_2 in equation (1), we get, y = a sin (ω_1 t − k_1 x) + a sin(ω_2 t − k_2 x) = 2 a [ sin ω_1 t . cos k_1 x - cos ω_1 t . sin k_1 x + sin ω_2 t . cos k_2 x - cos ω_2 t . sin k_2 x ] This is the resultant wave equation. Here resultant amplitude is 2a. Answer: The resultant waves formed group wave, amplitude is 2a and produces beats.
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