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 $3.4\text{cm}$

A wave repeats its cycle after a full time period or full wavelength.
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 $3.4\text{cm}$