Two sources of sound $S_1$ and $S_2$ are moving towards and away from a stationary observer with the same…

Two sources of sound $S_1$ and $S_2$ are moving towards and away from a stationary observer with the same speed, respectively. Observer detects 3 beats per second. Find the value of speed of sources (approximately). (Take, $f_1 = f_2 = 500\text{ Hz}$ and speed of sound in air $= 330\text{ ms}^{-1}$) [AIIMS 2019] Diagram shows source A moving right towards an Observer, and source B moving right away from the Observer, with '3 beats/s' indicated below the Observer.
  1. 1 ms$^{-1}$
  2. 2 ms$^{-1}$
  3. 3 ms$^{-1}$
  4. 4 ms$^{-1}$

Solution

Given, frequency of sound produced sources $S_1$ and $S_2$, i.e. $f_1 = f_2 = 500\text{ Hz}$ Speed of sound in air, $v = 330\text{ ms}^{-1}$ Beat frequency $= 3\text{ Hz}$ Let $v_s$ be the speed of source. When first source is moving towards the observer and $f_1'$ be apparent frequency heard by the observer, then $f_1' = \frac{v}{v - v_s} \times f_1 = \frac{330}{330 - v_s} \times 500$

Practice more Waves and Sound questions on Aicharya