Q.15.13 Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all:

  (a)\; y=2\; \cos (3x)\sin (10t)

(b)\; y=2\sqrt{x-vt}

(c)y=3\sin (5x-0.5t)+ 4\; \cos (5x-0.5t)

(d)\; y=\cos x\; \sin t+\cos 2x\: \sin \: 2t

Answers (1)
S Sayak

 (a)  It represents a stationary wave.

(b) The given function does not represent a wave as we can see at certain values of x and t the function would not be defined.

(c) It represents a travelling wave.

(d) It represents a stationary wave. It is a superposition of two stationary waves which ultimately results in another stationary wave.

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