Ncert Exercises & Solutions

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) $y = 2 \cos (3 x) \sin (10 t)$

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

(d) $y = cosxsint + \cos 2 xsin 2 t$

(a) The given equation represents a stationary wave because this equation is similar to

y = asin (kx) \cos (ωt) .

(b) The given equation is not a periodic function. Therefore, it does not represent either a travelling wave or a stationary wave.

(c) The given equation represents a travelling wave as the harmonic terms 'kx' and 'ωt' are in the combination of (kx–ωt).

(d) The given equation represents a stationary wave because this equation actually represents the superposition of two stationary waves similar to $y = asin (kx) \cos (ωt) .$

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