Question

A source (S) of sound has frequency 240 Hz. When the observer (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 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 Hz. The value of n is ______.

Answer 1

Correct answer is : 200

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 :

\(f_1=\left(\frac{C+V}{C-V}\right) f_S\)

\(288=\left(\frac{\mathrm{C}+\mathrm{V}}{\mathrm{C}-\mathrm{V}}\right) 240\)

Case-2 :

\(\mathrm{f}_2=\left(\frac{\mathrm{C}-\mathrm{V}}{\mathrm{C}+\mathrm{V}}\right) \mathrm{f}_{\mathrm{s}}\)

\(\mathrm{n}=\left(\frac{\mathrm{C}-\mathrm{V}}{\mathrm{C}+\mathrm{V}}\right) 240\)

multiply the two equations, we get.

(288) (n) = (240) (240) 

N = 200