Given that` y = A sin [((2 pi )/(lambda)(ct - x))]` where` y` and `x` are measured in metres ,Which of the following statements is true ?

Options

A. The unit of `lambda` is same as that of x and A
B. The unit of `lambda` is same as that of x but not A.
C. The unit of c is same as that of `(2pi)/(lambda)`
D. The unit of `(c-t)` is same as that of `(2pi)/(lambda)`

Answer

C

Explanation

Here, unit of A is same as unit of y because `sin theta` is dimensionless for all `theta`. Given unit of x and y both are metres.
So, such of A is same as unot of x. AS `(2pi)/(lambda) ct -2pi (x)/(lambda)` is dimensionless, so x and `lambda` have same units.
`A, x, lambda` have same units. The unit of C is m/s.