A sound source is approaching the listener. The frequency of sound is $100\text{ cps}$ while passing through…
A sound source is approaching the listener. The frequency of sound is $100\text{ cps}$ while passing through the listener, it is $50\text{ cps}$. The frequency when the observer moves with the source is [UP CPMT 2015]
$77.3\text{ Hz}$
$66.67\text{ Hz}$
$63.33\text{ Hz}$
$133.3\text{ Hz}$
Solution
From formula of Doppler's effect,
$f' = f \left(\frac{v}{v - v_s}\right) \Rightarrow 100 = \frac{fv}{v - v_s}$
$\Rightarrow v - v_s = \frac{fv}{100}$ … (i)
In case of recession of source, $f' = f \left(\frac{v}{v + v_s}\right) \Rightarrow 50 = \frac{fv}{v + v_s}$
$\Rightarrow v + v_s = \frac{fv}{50}$ … (ii)
From Eqs. (i) and (ii), we get
$2v = \frac{3fv}{100}$
$\therefore f = \frac{200}{3} = 66.67\text{ Hz}$