The equation of the stationary wave is
`y = 2 A sin (( 2 pi c t)/( lambda)) cos (( 2 pi x)/( lambda))`
Which of the following statements is wrong?

Options

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

Answer

D

Explanation

Dimensions of `(2pict)/(lambda) =M^(0)L^(0)T^(0)`
`ct=M^(0)L^(1)T^(0)`
`ct=[L^(1)] = lambda`
Dimensions of `(2pix)/(lambda) =M^(0)L^(0)T^(0)`
{because angle has no dimension}
`x=M^(0)L^(1)T^(0)`
`x=[L^(1)] =lambda`
Dimensions of `(2pic)/(lambda) =(L^(1)T^(-1))/(L^(1))`
Dimension of `(2pix)/(lambdat)=(L^(1)T^(-1))/(L^(1))`
`[:. 2pi " is dimensionless"]`
so dimensions are equal ltbegt Dimensions of `(c)/(lambda) ne` Dimensions of `(x)/(lambda)`
`:. (L^(1)T^(-1))/(L^(-1)) ne (L^(1))/(L^(1))`