### Theory:

The distance travelled by a sound wave per unit time as it propagates through an elastic medium is known as the speed of sound.

$\mathit{Speed}\left(v\right)=\frac{\mathit{Distance}}{\mathit{Time}}$

If one wavelength ($\mathrm{\lambda }$) represents the distance travelled by one wave, and one time period ($$T$$) represents the time taken for this propagation, then

$\mathit{Speed}\left(v\right)\phantom{\rule{0.147em}{0ex}}=\frac{\mathit{One}\phantom{\rule{0.147em}{0ex}}\mathit{wavelength}\left(\mathrm{\lambda }\right)}{\mathit{One}\phantom{\rule{0.147em}{0ex}}\mathit{time}\phantom{\rule{0.147em}{0ex}}\mathit{period}\left(T\right)}$

And, we know

$T=\frac{1}{v}$

By applying this in speed formula, we get

$v=n\mathrm{\lambda }$

Under the same physical conditions, the speed of sound in a given medium remains nearly constant for all frequencies.

Let us solve following example for better understanding.

Example:

A sound wave has a frequency of $$2$$ $$kHz$$ and a wavelength of $$15$$ $$cm$$. How much time will it take to travel $$1.5$$ $$km$$?

Given data:

Frequency $$=$$ $$2$$ $$kHz$$ $$=$$ $$2000$$ $$Hz$$

Wavelength $$=$$ $$15$$ $$cm$$ $$=$$ $$0.15$$ $$m$$

Distance $$=$$ $$1.5$$ $$km$$ $$=$$ $$1500$$ $$m$$

To find: Time period

Formula:$\mathit{Time}=\frac{\mathit{Distance}}{\mathit{Speed}}$

We don't know the value of speed,

$v=n\mathrm{\lambda }$

$\begin{array}{l}v=2000×0.15\\ =300\phantom{\rule{0.147em}{0ex}}m/s\end{array}$

Now, apply in the value of speed in time formula

$\begin{array}{l}\mathit{Time}=\frac{1500}{300}\\ =5\phantom{\rule{0.147em}{0ex}}s\end{array}$

The sound will take $$5$$ $$s$$ to travel a distance of $$1.5$$ $$km$$.