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Mechanical Properties Of Fluids

Question
CBSEENPH11018908

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 

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(c) y = 3 sin(5x –0.5t) + 4 cos(5x – 0.5t) 

(d) y = cos x sin t + cos2x sin2t.

Solution

(a) The equation represents a stationary wave. 
(b) The equation does not represent any wave. 
(c) We have,
 y = 3sin(5x–0.5t) + 4cos(5x – 0.5t) = 5 sin [5x – 0.5t + tan-1 (4/3)].
This is an equation for a travelling wave. 
(d) y = cos x sin t + cos 2xsin 2t, is the equation for superposition of two stationary waves.