# Two waves, travelling along the same direction, are given by y1 (x, t)=a sin (ω1t- k1x) y2 (x, t)=a sin (ω2t-k2x) Suppose that ω1 and k1 are respectively slightly greater than 2ωand k2 i) Obtain an expression for the resultant wave arising due to their superposition and ii) explain the formation of wave packets.

1
by torcher

2015-09-25T22:52:41+05:30

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W1 =  w2 + 2 w          and    k1 = k2 + 2 k

y1 =  a Sin (w1 t - k1 x)
y2 = a Sin (w1 t - k1 x - 2 w t + 2 k x)

y1 + y2  = a 2 Sin [ w1t - k1 x -  w t + k x]  Cos (w t - k x)

The resulting wave have frequency as  (w1 + w2) /2
then wave number too is the average...
there is an envelope that envelops the wave.
Its amplitude is given by    2 a  cos (wt - k x)  this  is a slow varying wave with small frequency and large wavelength.