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=2cos(3x)sin(10t)` (b) `y=2sqrt(x-vt)`
(c) `y=3sin(5x-0.5t)+4cos(5x-0.5t)` (d) `y=cosx sint +cos2x sin2t`

Explanation

(a) It represents a stationary wave because it has two harmonic functions of x and t separately.
(b) It does not represent a stationary wave or any other wave because it contains no harmonic functions of x and t.
(c) It represents a travelling harmonic wave because it has two harmonic functions of x and t.
(d) The given equation is a superposition of two stationary waves. Therefore, it represents a stationary wave.