Question

A person is listening to a tone of $500Hz$ sitting at a distance of $450m$ from the source of the sound. What is the distance between successive compressions from the source? The velocity of sound is $344m{s}^{-1}$.

Answer 1

Step 1: Given:

Frequency, $\nu =500Hz$

Velocity, $\upsilon =344m{s}^{-1}$

Distance between source and observer, $d=450m$

Step 2: Calculate the wavelength:

$\lambda =\frac{\upsilon }{\nu }$ …… (Here, $\lambda$ is the wavelength)

$$\begin{gathered} \lambda =\frac{344m{s}^{-1}}{500Hz} \\ \lambda =0.688m \end{gathered}$$

Thus, the wavelength is $0.688m$.

Step 3: Calculate the distance between successive compressions:

Since the distance between source and observer is $450m$, the no. Of consecutive compressions, the observer is away from are

Distance between two successive compressions$=\frac{450m}{0.688m}$

Distance between two successive compressions$=654m$

Thus, the distance between two successive compressions is $654m$.