Question

A source and a detector move away from each other, each with a speed of $10{\text{ms}}^{-1}$ with respect to the ground, with no wind. If the detector detects a frequency $1950\text{Hz}$ of the sound coming from the source, what is the original frequency of the source ?
Speed of sound in air $=340{\text{ms}}^{-1}$.

• A. $2020\text{Hz}$
• B. $2050\text{Hz}$
• C. $2070\text{Hz}$
• D. $2090\text{Hz}$

Answer 1

The correct option is C $2070\text{Hz}$

Let the original frequency of the source be $f_0$.

Given,
Apparent frequency, $f=1950\text{Hz}$
Speed of observer (detector),$v_0=10{\text{ms}}^{-1}$
speed of source, $v_s=10{\text{ms}}^{-1}$
Speed of sound, $v=340{\text{ms}}^{-1}$

As both the source and the detector are moving away from each other, the apparent frequency is given by,

$f=f_0\left(\frac{v-v_0}{v+v_S}\right)$

$\Rightarrow 1950=\left(\frac{340-10}{340+10}\right)\times f_0$

$\therefore f_0=1950\times \frac{35}{33}=2068\approx 2070\text{Hz}$

Hence, option $\left(\text{C}\right)$ is correct.