### Q.13:- 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)

(b)

(c)

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

*y*= 2 √*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*

**Answer:-**

(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.