The displacement of particles in a string stretched in the x-direction is represented by y.among the following expressions for y, those describing wave motion are

Options

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))`.

Answer

A, C

Explanation

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.