A person with vibrating tuning fork of frequency $338\text{ Hz}$ is moving towards a vertical wall with a…
A person with vibrating tuning fork of frequency $338\text{ Hz}$ is moving towards a vertical wall with a speed of $2\text{ ms}^{-1}$. Velocity of sound in air is $340\text{ ms}^{-1}$. The number of beats heard by that person per second is [KCET 2013]
$2$
$4$
$6$
$8$
Solution
As the person having tuning fork is moving towards a wall, therefore $v_s = v_o = 2\text{ ms}^{-1}$ (Given)
So, $\frac{f'}{f} = \frac{v + v_o}{v - v_o}$
$\Rightarrow \frac{f' - f}{f} = \frac{v + v_o - v + v_o}{v - v_o}$
$\Rightarrow \frac{\Delta f}{f} = \frac{2v_o}{v - v_o}$
$\Delta f = \frac{2v_o}{v - v_o} \times f = \frac{2 \times 2 \times 338}{(340 - 2)} = 4\text{ Hz}$
$\therefore$ Number of beats heard $= 4$