Check the dimensional of the wave y = sin (x - vt) . If it is dimensionally wrong , write the above equation in the correct form .

Explanation

Dimensionally it is not correct . We know that y = sin (x - vt) must be a dimensionless quantity but x- vt has dimensional . The correct equation is y = sin `( kx - omega t)` , where k and `omega` have dimensions of inverse of length and inverse of time respectively . The sine functions and cosine functions are periodic functions with period `2pi` . Therefore , the correct expression is `y = sin ((2pi)/(lambda) x - (2 pi)/(T) t)` where `lambda` and T are wavelength and time period , respectively . In general , y (x , t) = A sin (k x - `omega` t) .