A source (S) of sound has frequency $240 \mathrm{~Hz}$. When the observer $(\mathrm{O})$ and the source move…
A source (S) of sound has frequency $240 \mathrm{~Hz}$. When the observer $(\mathrm{O})$ and the source move towards each other at a speed $v$ with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be $288 \mathrm{~Hz}$. However, when the observer and the source move away from each other at the same speed $v$ with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be $n \mathrm{~Hz}$. The value of $n$ is ______
Solution
Frequency received by observer $f_0=\left(\frac{C \pm V_0}{C \pm V_S}\right) f_{\mathrm{s}}$, C is speed of sound
Case-1:
$\begin{aligned} & \mathrm{f}_1=\left(\frac{\mathrm{C}+\mathrm{V}}{\mathrm{C}-\mathrm{V}}\right) \mathrm{f}_{\mathrm{s}} \\ & 288=\left(\frac{\mathrm{C}+\mathrm{V}}{\mathrm{C}-\mathrm{V}}\right) 240\end{aligned}$
Case-2:
$f_2=\left(\frac{C-V}{C+V}\right) f_S$
$\mathrm{n}=\left(\frac{\mathrm{C}-\mathrm{V}}{\mathrm{C}+\mathrm{V}}\right) 240$
multiply the two equations, we get.
$\begin{aligned} & (288)(\mathrm{n})=(240)(240) \\ & \mathrm{n}=200\end{aligned}$
.
