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

(a) *y *= 2 cos (3*x*) sin (10*t*)

(b) `y = 2sqrt(x- vt)`

(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*

#### Solution 1

**(a)** The given equation represents a stationary wave because the harmonic terms *kx*and ω*t* 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 ω*t*are in the combination of *kx* – ω*t*.

**(d)** The given equation represents a stationary wave because the harmonic terms *kx*and ω*t* appear separately in the equation. This equation actually represents the superposition of two stationary waves.

#### Solution 2

(a) It represents a stationary wave.

(b) It does not represent either a travelling wave or a stationary wave.

(c) It is a representation for the travelling wave.

(d) It is a superposition of two stationary wave.