Question

phase difference between twe interfering waves at a point is 3π/2. The path difference between these two waves at that poin is

Answer 1

The phase difference between two interfering waves is given as $\frac{3\pi}{2}$

Let the phase difference is denoted as $d\theta\ = \frac{3\pi}{2}$

We are asked to calculate the path difference.

Let the path difference is denoted as dx.

We know that $2\pi\ radian\ =\ \lambda$

                       $1 rad=\frac{\lambda}{2\pi}$

                       $d\theta=\frac{\lambda}{2\pi}\times d\theta$

Hence, path difference= $\frac{\lambda}{2\pi}\times phase\ difference$

                                    dx  = $\frac{\lambda}{2\pi}\times d\theta$

                                      = $\frac{\lambda}{2\pi}\times \frac{3\pi}{2}$

                                      = $\frac{3\lambda}{4}$

Hence, the path difference at that point is $\frac{3\pi}{4}$