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Question -

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 traveling wave, (ii) a stationary wave or (iii) none at all:
(a) y = 2 cos (3x) sin (10t)
(b)  
(c) y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t)
(d) y = cos x sin t + cos 2x sin 2t



Answer -

(a) The given equation represents a stationary wavebecause the harmonic terms kx and ωt appearseparately in the equation.

(b) The given equation does not contain any harmonicterm. Therefore, it does not represent either a travelling wave or a stationarywave.

(c) The given equation represents a travelling wave asthe harmonic terms kx and ωt are in thecombination of kx – ωt.

(d) The given equation represents a stationary wavebecause the harmonic terms kx and ωt appearseparately in the equation. This equation actually represents the superpositionof two stationary waves.

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