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The displacement of partcles in a string...

The displacement of partcles in a string streched in the x-direction is by `y`. Among the following expressions for `y`, those describing wave motion are :

A

`coskxsinomegat`

B

`k^(2)x^(2)-sinomega^(2)t^(2)`

C

`cos^(2)(kx+omegat)`

D

`cos(k^(2)x^(2)-omega^(2)t^(2))`.

Text Solution

Verified by Experts

The correct Answer is:
A, C
For wave motion, the differential equation is
`(partial^(2)y)/(partialt^(2))(constant(omega^(2))/k^(2))(partial^(2)y)/(partialx^(2))`
or `(partial^(2)y)/(partialt^(2))=v^(2)(partial^(2)y)/(partialx^(2))`……(i)
The wave motion is characterized by the two condition VIZ
f(x.t)=f(x,t+T)....(ii)
`f(x,t)=f(x+lambda,t)`.....(iii)
Hence option (A) and (C) represent correct answer.
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