Question

A tuning fork producing sound of frequency $380\text{Hz}$ is moving towards a wall with a velocity of $4{\text{ms}}^{-1}$. The number of beats per second heard by a stationary listener produced due to direct and reflected sounds will be
[speed of sound in air $=340{\text{ms}}^{-1}$]

• A. $6$
• B. $0$
• C. $7$
• D. $5$

Answer 1

The correct option is B $0$

For sound approaching the wall, the apparent frequency will be,
$f^{{}^{\prime }}=f_0\left(\frac{v+v_0}{v-v_s}\right)$
$\Rightarrow f^{{}^{\prime }}=380\times \left(\frac{340+0}{340-4}\right)$
$\Rightarrow f^{{}^{\prime }}=384\text{Hz}$ ...........(1)
This will be the frequency of sound reflected by the wall. And as the listener is also at rest, so the same frequency will be heard by it after reflection.
Also, for sound approaching the stationary listener directly, the apparent frequency will be,
$f^{{}^{\prime \prime }}=f_0\left(\frac{v+v_0}{v-v_s}\right)$
$\Rightarrow f^{{}^{\prime \prime }}=380\times \left(\frac{340+0}{340-4}\right)$
$\Rightarrow f^{{}^{\prime \prime }}=384\text{Hz}$ ...........(2)
Now, beat frequency,
$f_b=|f_1-f_2|=384-384=0$
[from (1) and (2)]
Hence, $0$ beat per second will be heard by stationary listener produced due to direct and reflected sounds.