Question 18 of 23intermediate🔍 AnalyzeShort Answer3 marks

Given below are some functions of xx and tt 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=2cos⁡(3x)sin⁡(10t)y = 2 \cos(3x) \sin(10t)

Answer

Stationary wave

(b)

y=2x−vty = 2\sqrt{x - vt}

Answer

None at all

(c)

y=3sin⁡(5x−0.5t)+4cos⁡(5x−0.5t)y = 3 \sin(5x - 0.5t) + 4 \cos(5x - 0.5t)

Answer

Travelling wave

(d)

y=cos⁡xsin⁡t+cos⁡2xsin⁡2ty = \cos x \sin t + \cos 2x \sin 2t

Answer

None at all

Explanation

For a travelling wave, the displacement function must be of the form y(x,t) = a sin(kx - ωt + φ) or similar, where x and t appear together in the argument. For a stationary wave, the spatial and temporal parts are separated multiplicatively, like y(x,t) = A sin(kx) cos(ωt).

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