Question

A source s emitting sound of $400Hz$ is fixed on block A which is attached to free end of a spring $S_A.$ The detector $D$ fixed on block $B$ attached to the free end of spring $S_B$ detects this sound. The blocks A and B are simultaneously displaced towards each other through a distance of $1.0m$ and then left to vibrate. If vibrational frequency of each block is $3Hz,$ the maximum frequencies of sound detected by D is $nhz$ . Then, what is the value of $n$ ?
$\left(v_{\text{sound }}=340m/s\right)$

Answer 1

Answer: 448

$\omega =2\pi v=2\pi (3)=6\pi$
$\therefore \omega =18.85rad{s}^{-1}$
Maximum speed of motion of $\left|v_A\right|$ and $\left|v_B\right|=A\omega$
$f_{max}=\left(\frac{v+v_B}{v-v_A}\right)f=\left(\frac{340+A\omega }{340-A\omega }\right)f$
$=\left(\frac{340+18.85}{340-18.85}\right)400$
$=\left(\frac{358.85}{321.15}\right)\times 400$
$=1.12\times 400$
$\therefore f_{max}=448Hz$