The equation of a simple harmonic progressive wave is given by y = A sin `(100 pi t - 3x)` . Find the distance between 2 particles having a phase difference of `(pi)/(3)`.

Options

A. `(pi)/(9) m`
B. `(pi)/(3) m`
C. `(pi)/(6) m`
D. `(pi)/(18) m`

Answer

A

Explanation

`y = A sin (100 pi t- 3x)`
`= A sin 2pi (50 t - (3x)/(2pi))`
Comparing this with the standard equation,
`y = A sin 2pi ((t)/(T) - (x)/(lamda))`, we get
`(3x)/(2pi) = (x)/(lamda) :. lamda = (2pi)/(3)`
and `:'` Phase difference `= (2pi)/(lamda)` (path difference)
`:. (pi)/(3) = (2pi)/((2pi)/(3))` (path difference)
`:. (pi)/(3) = 3` (path difference)
`:.` Path difference `= (pi)/(9) m`