A detector is released from rest over a source of sound of frequency $f_o = 10^3\text{ Hz}$. The frequency…
A detector is released from rest over a source of sound of frequency $f_o = 10^3\text{ Hz}$. The frequency observed by the detector at time $t$ is plotted in the graph. The speed of sound in air is
(Take, $g = 10\text{ ms}^{-2}$)
(a) $330\text{ ms}^{-1}$
(b) $350\text{ ms}^{-1}$
(c) $300\text{ ms}^{-1}$
(d) $310\text{ ms}^{-1}$
Solution
Frequency, $f = f_o \left( \frac{v + v_o}{v} \right) = 10^3 \left( 1 + \frac{v_o}{v} \right)$
$= 10^3 + \frac{10^3}{v} (gt)$
$= 10^3 + \left( \frac{10^4}{v} \right) t \quad (\because v_o = gt)$
Slope of $f\text{-}t$ line should be equal to $\frac{10^4}{v}$.
$\therefore \quad \frac{1000}{30} = \frac{10^4}{v} \quad \text{or} \quad v = 300\text{ ms}^{-1}$
