Two point sources of sound are separated by 10 cm . They vibrate in...

Let the two point sources be $S_1$ and $S_2$, and the observation point be $P$.

The point $P$ is located on the perpendicular bisector of the line joining the two sources. By the geometric property of a perpendicular bisector, any point on it is equidistant from both the sources.

Given that the distance of point $P$ from one source is $20 \text{ cm}$, its distance from the other source must also be $20 \text{ cm}$.

$S_1P = 20 \text{ cm}$

$S_2P = 20 \text{ cm}$

The path difference $\Delta x$ between the two waves reaching point $P$ is:

$\Delta x = S_1P - S_2P = 20 \text{ cm} - 20 \text{ cm} = 0$

The phase difference $\Delta \phi$ is related to the path difference by the formula:

$\Delta \phi = \dfrac{2\pi}{\lambda} \Delta x$

Substituting $\Delta x = 0$:

$\Delta \phi = \dfrac{2\pi}{5.0} \times 0 = 0$

Since the sources vibrate in phase, the initial phase difference is also zero. Thus, the total phase difference at point $P$ is $0$.