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=3sin(5x-0.5t)+4cos(5x-0.5t)` (c) `y=cosx sint +cos2x sin2t`

Explanation

(a) The given equation represents a stationary wave because the harmonic terms kx and ωt appear separately in the equation.
(b) The given equation does not contain any harmonic term. Therefore, it does not represent either a travelling wave or a stationary wave.
(c) The given equation represents a travelling wave as the harmonic terms kx and ωt are in the combination of kx `-omegat`.
(d) The given equation represents a stationary wave because the harmonic terms kx and ωt appear separately in the equation. This equation actually represents the superposition of two stationary waves.