Question

A tuning fork with a time period of $\frac{1}{256}\text{s}$ produces a sound wave in which the separation between adjacent compression and rarefaction is $0.7\text{m}$. Then, the speed of sound wave is

• A. $250\text{m/s}$
• B. $400\text{m/s}$
• C. $310\text{m/s}$
• D. $358\text{m/s}$

Answer 1

The correct option is D $358\text{m/s}$

Distance between adjacent compression and rarefaction is equal to half of the wavelength as we can see below.


Given that the separation between adjacent compression and rarefaction is $0.7\text{m}$, the wavelength is twice the separation.

So, $\lambda =0.7\times 2=1.4\text{m}$

We know that velocity of sound wave is given by,

$v=\frac{\lambda }{T}$

where $\lambda$ is wavelength and $T$ is time period.

$\Rightarrow v=\frac{1.4\times 256}{1}=358\text{m/s}$