Waves
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Question : 13
Total: 27
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 √ x − v t
(c)y = 3 sin ( 5 x − 0.5 t ) + 4 cos ( 5 x − 0.5 t )
(d)y = cos x sin t + cos 2 x sin 2 t
(a)
(b)
(c)
(d)
Solution:
(a) This equation has two harmonic functions of each x and t separately, so it represents stationary wave.
(b) This function does not represent any wave as it contains no harmonic function.
(c) It represents progressive/travelling harmonic wave as the arguments of cosine and sin functions are same.
(d) This equation is the sum of two functionscos x sin t cos 2 x sin 2 t
(b) This function does not represent any wave as it contains no harmonic function.
(c) It represents progressive/travelling harmonic wave as the arguments of cosine and sin functions are same.
(d) This equation is the sum of two functions
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