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 travelling wave, (ii) a stationary wave or (iii) none at all : 

(a) y = 2 cos (3x) sin (10 t) 

(b) y = 2√x - vt 

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

(d) y = cos x sin t + cos 2x sin 2t

Answer 1

(a) The given function is the product of two reparate harmonic functions of x and t, so it represents a stationary wave. 

(b) If does not satisfy the differential equation of wave so it will not represents any type of wave. 

(c) The given functions can be expressed in the form

So, it will represent a travelling wave. 

(d) If represents the superposition of two stationary waves; one represented by cos x sin t and other by cos 2x sin 2t.