Question

Give below are some functions of x and t to represesnt the displacement of an elastic wave.
`(i) ``y=5cos (4x) sin (20t)`
(ii) `y=4sin(5x-t//2)+3cos(5x-t//2)`
(iii) `y=10cos[(252-250)pit]cos[(252+2500pit]` (iv)` y=100cos(100pit+0.5x)`
State which of these represent
(a) a travelling wave along-x direction
(b) a stationary wave
(c) beats
(d) a travelling wave along `+x` direction
Give reasons for your answers.

Answer 1

The four given equations are:
(i) `y=5cos 4xsin20t`
(ii) `y=4sin(5x-t//2)+3cos(5x-t//2)`
(iii) `y=10cos(252-250)pit cos(252+250)pit`
(iv) `y=100cos(100pit +0.5x)`
From the basic concepts , we know
(a) Eqn. (iv) represents a wave travelling along `-x` direction.
(b) Eqn. (i) represents a stationary wave as terms containing x and t are independent.
(c) Eqn. (iii) represents beats involving sum and difference of two frequencies 252 and 250.
(d) Eqn. (ii) represents a wave travelling along `+x ` direction.