The equation of a stationary wave is `y=2A sin((2pict)/lambda) cos ((2pix)/lambda)`
Which of the following is correct?

Options

A. The unit of ` c t` is same as that of `lambda`.
B. The unit of ` x` is same as that of `lambda`.
C. The unit of `2 pi c // lambda` is same as that of ` 2 pi x // lambda t`.
D. The unit of ` c// lambda` is same as that of ` x // lambda`.

Answer

D

Explanation

Here `( 2 pi ct // lambda)` as well as `( 2 pi x // lambda)`are dimensionless . So unit of `ct` is same as that of `x` is same as that of `lambda` . Also ,
`[( 2 pi ct)/( lambda)] = [ ( 2 pi x)/( lambda)] = M^(0) L^(0) T^(0)`
Hence,`[( 2 pi c)/( lambda)] = [ ( 2 pi x)/( lambda t )]` . In option (d) , `x // lambda` is unitless. This is not the case with `c// lambda`.