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

Let the two sources be $S_1$ and $S_2$ with a separation $d = 10 \text{ cm}$.

The point $P$ is located on the line passing through $S_1$ and $S_2$ at a distance of $20 \text{ cm}$ from one of the sources. Since $20 \text{ cm} > 10 \text{ cm}$, the point $P$ lies outside the segment $S_1 S_2$.

For any point on the line outside the segment connecting the two sources, the path difference $\Delta x$ between the waves from the two sources is exactly equal to the distance between the sources.

$\Delta x = |S_1 P - S_2 P| = d = 10 \text{ cm}$

The phase difference $\Delta \phi$ is given by the relation:

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

Substituting $\lambda = 5.0 \text{ cm}$ and $\Delta x = 10 \text{ cm}$:

$\Delta \phi = \dfrac{2\pi}{5.0} \times 10 = 4\pi$

A phase difference of $4\pi$ is an integer multiple of $2\pi$, which is equivalent to a phase difference of $0$.