One end of a taut string of length 3m along the x axis is fixed at x = 0. The speed of the waves in the…

One end of a taut string of length 3m along the x axis is fixed at x = 0. The speed of the waves in the string is 100 ms-1 . The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)
  1. yt=Asin⁡πx6cos⁡50πt3
  2. yt=A sin⁡πx3cos⁡100πt3
  3. yt=Asin⁡5πx6cos⁡250 πt3
  4. yt=Asin⁡5πx2cos⁡250 πt

Solution

Taking y(t) = A f(x) g(t) & Applying the conditions:
1; here x = 3m is antinode & x = 0 is node
2; possible frequencies are odd multiple of fundamental frequency.
Where, vfundamental=v4l=253Hz
The correct option are A, C, D.

Asked in: JEE Advanced 2014 (Paper 1)

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