Question

# A small source of sound vibrating at frequency 500 Hz is rotated in a circle of radius 100/π cm at a constant angular speed of 5.0 revolutions per second. A listener situation situates himself in the plane of the circle. Find the minimum and the maximum frequency of the sound observed. Speed of sound in air = 332 m s−1.

Solution

## Given: Speed of sound in air v = 332 ms−1 Radius of the circle r = $\frac{100}{\mathrm{\pi }}$ cm = $\frac{1}{\mathrm{\pi }}$ m Frequency of sound of the source ${f}_{0}$ = 500 Hz Angular speed $\omega$ = 5 rev/s Linear speed of the source is given by:  $v=\omega r$ ⇒   ∴ velocity of source ${v}_{s}$ = 1.59 m/s Let X be the position where the observer will listen at a maximum and Y be the position where he will listen at the minimum frequency. Apparent frequency $\left({f}_{1}\right)$ at X is given by: ${f}_{1}=\left(\frac{v}{v-{v}_{s}}\right){f}_{0}$ On substituting the values in the above equation, we get: Apparent frequency $\left({f}_{2}\right)$ at Y is given by: ${f}_{2}=\left(\frac{v}{v+{v}_{s}}\right){f}_{0}$ On substituting the values in the above equation, we get: PhysicsHC Verma - IStandard XI

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