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 10t
(b)
(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.