Question

A sound wave of frequency $10\text{kHz}$ is travelling in air with speed of $340\text{m/s}$. Find the minimum separation between two points in the medium where the phase difference is $2\pi$.

• A. $3.4\text{cm}$
• B. $6.8\text{cm}$
• C. $1.7\text{cm}$
• D. $5.1\text{cm}$

Answer 1

The correct option is A $3.4\text{cm}$

In this question we have to find the minimum separation between two points where the phase difference is $2\pi$. That means, we have to determine the path difference between the points.

A wave repeats its cycle after a full time period or full wavelength. We can thus, write the relation between path difference and phase difference as

$\text{Phase difference}=\frac{2\pi }{\lambda }\times \text{Path Difference}$

As here the phase difference is given as $2\pi$ so,

$2\pi =\frac{2\pi }{\lambda }\times \text{Path Difference}$

$\Rightarrow \text{Path difference}=\lambda$

Hence, two points separated by minimum distance of $\lambda$ will be having a phase difference of $2\pi$.

We know that velocity of sound wave is given by,

$v=\lambda f$

where $\lambda$ is wavelength and $f$ is frequency.

$\Rightarrow \lambda =\frac{v}{f}$

$\Rightarrow \lambda =\frac{340}{10\times {10}^3}=3.4\times {10}^{-2}\text{m}=3.4\text{cm}$

So, minimum separation between two points in the medium is $3.4\text{cm}$