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

Answers

The Brainliest Answer!
2015-09-25T22:52:41+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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.

2 5 2