The equation of a simple harmonic progressive wave is given by `y = 12 sin (omega t-4x)`m. What is the distance between 2 particles on the wave, having a phase difference of `pi//2` ?

Options

A. `pi//2m`
B. `pi//4 m`
C. `pi//6 m`
D. `pi//8 m`

Answer

D

Explanation

`y = 12 sin (omega t - 4x)`
`= 12 sin ((2pi )/(T) t - 4x)`
`= 12 sin 2pi ((t)/(T) - (4x)/(2pi))`
`= 12 sin 2pi ((t)/(T) - (2x)/(pi))`
Comparing this with the equation.
`y = A sin 2pi ((t)/(T) - (x)/(lamda))`
We get `(x)/(lamda) = (2x)/(pi) :. lamda = pi//2`
But phase difference `= (2pi)/(lamda)` (path difference)
`:. (pi)/(2) = (2pi)/(pi//2)` (path difference) = 4 (path difference)
`:.` Path difference `= (pi)/(2 xx4) = (pi)/(8) m`