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:

1. y = 2 cos (3x) sin (10t)

2. y = 2 √(x -vt) 

3. y = 3 sin(5x – 0.5t) + 4cos(5x-0.5t) 

4. y = cos x sin t + cos 2x sin 2t

Answer 1

1. y = 2cos (3x) sin (10 t)

Represents a stationary wave

2. y = 2 √(x -vt) 

Does not represent any wave.

3. y = 3 sin (5x – 0.5 t) + 4 cos (5x – 0.5t)

= [5 sin [5x - 05t -tan^-1 (3/4)] Represents a travelling wave,

4. y = cos x sin t + cos 2x sin 2t 

Represents superposition of 2 stationary waves.