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.
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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.
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.
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