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A wave y = a sin (omegat - kx) on a stri...

A wave `y = a sin (omegat - kx)` on a string meets with another wave producing a node at `x = 0`. Then the equation of the unknown wave is

A

`y=- a sin (omega t-Kx)`

B

`y=a sin (omega t-Kx)`

C

`y= -a sin (omega t+ Kx)`

D

`y= a sin (omega t+ Kx)`

Text Solution

Verified by Experts

The correct Answer is:
C
The equation ` y = a sin ( omega t - K x)` represents a wave travelling from left to right along `.^(+)ve` X - axis.
For forming a node at ` x = 0 ` , the other wave should satisfy two condition.
(i) It should travel from right to left (i.e. `omegat - Kx`) will become `(omegat + Kx)`.
(ii) The amplitude will change from a to - a .
` :. ` The equation of the unknown wave will be
` y = - a sin ( omega t + Kx )`
[ With ` y = a sin ( omega t + Kx`), we get an antinode at x = 0 ]
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