Question

A small source of sound vibrating at frequency $500Hz$ is rotated in a circle of radius $100/\pi cm$ at a constant angular speed of $5.0$ revolutions per second. The speed of sound in air is $330m/s$.
If the observer moves towards the source with a constant speed of $20m/s$ , along the radial line to the centre , the fractional change in the apparent frequency over the frequency that the source will have if considered at rest at the centre will be

• A. $6$ %
• B. $3$ %
• C. $2$ %
• D. $9$ %

Answer 1

The correct option is A $6$ %

The frequency of the source considered stationary at the centre is $n_0=500Hz$ when the observer moves towards the centre with constant speed $u$ , the apparent frequency is
$n_a=\left(\frac{V+u}{V}\right)500=\frac{330+20}{330}\times 500=\frac{35}{33}\times 500$
Change in frequency is given by
$n_a-n_0=(\frac{35}{33}\times 500-500)=\frac{2\times 500}{33}hz$
Fractional change of frequency is
$\left(\frac{n_a-n_0}{n_0}\right)=\left(\frac{2\times 500}{33}\right)\times \frac{1}{500}$
$=\frac{2}{33}=0.06$
Hence , percentage change is $6$ %