Does the wave function `y=A_(0) cos^(2)(2pi f_(0)t-2pix//lambda_(0)` represent a wave? If yes, the determine its amplitude frequency, and wavelength.

Explanation

Any wave function represents a wave if it satisfies the equation ltbRgt ` (del^(2)y)/(delx^(2))=(1)/(v^(2))(del^(2)y)/(delt^(2)`
It can be easily proved that the given wave function satisfies the above equation. Furthermore, it can be easily put in the form `y=f(x-vt)`. thus, it represent a wave. the amplitude, frequency, and wavelength of the wave are `A_(0)//2,2f_(0)` and `lambda_(0)//2`, respectively. it is because, the given function can be reduced to
`y=(A_(0))/(2)[1+cos{2(2pif_(0)t-(2pix)/(lambda_(0))}]`
`(A_(0))/(2)[1+cos[2pi(2f_(0))t-(2pix)/(lambda_(0)//2)]]`