A progressive wave is given by `y(x,l) = B cos (300 t - 0 . 15 x)` where x and y are in cm and t in second . What is the (i) direction of propagation, (ii) wavelength , (iii) frequency, (iv) wave speed and (v) phase difference between two points 0 . 2 m apart ?

Explanation

`y (x , l) - B cos (300 t - 0 . 15 x) `
Comparing this equation with stationary wave equation
`y - a cos 2 pi ((l)/(T)-(x)/(lambda))` , we have ,
(i) Direction of propagation is + x - axis
(ii) `(2pi)/(lambda) = 0 . 15 or, lambda = (2pi)/(0 . 15) = 41 . 87 ` ,
(iii) `(2pi)/(T) = 300 or, 2 pi n = 300`
(iv)or, `n = (300)/(2pi) = 47 . 78 ` Hz
`Deltaphi = (2pi)/(lambda)Delta x = (2pi)/(lambda) xx 0 . 2 `
`= (2 pi xx 0 . 2 xx 0 . 15)/(2 pi) = 0 . 03 ` rad