A source $S$ emitting sound of frequency $288 \mathrm{~Hz}$ is fixed on block $B$ which is attached to the…
A source $S$ emitting sound of frequency $288 \mathrm{~Hz}$ is fixed on block $B$ which is attached to the free end of a spring $S_2$ and an observer $O$ is on block $A$ which is attached to the free end of spring $S_1$ as shown in the figure. The blocks $A$ and $B$ are simultaneously displaced towards each other through a distance of $0.5 \mathrm{~m}$ and then left to oscillate. If the angular velocity of each blocks is $40 \mathrm{rad} \mathrm{s}^{-1}$, then the maximum frequency observed by the observer is (speed of sound in air is $340 \mathrm{~ms}^{-1}$ )
288 Hz
310 Hz
324 Hz
256 Hz
Solution
Frequency is maximum, when both $O$ and ' $S$ ' are moving towards each other with maximum speeds.
Now, maximum speed of $O=$ maximum speed of $S$ [and these two occur together].
$
=v_m=a \omega=0.5 \times 40=20 \mathrm{~ms}^{-1}
$
So, maximum frequency
$
\begin{aligned}
& =f_{\max }=f\left(\frac{v_{\text {sound }}+v_{\text {observer }}}{v_{\text {sound }}-v_{\text {source }}}\right)=288 \times\left(\frac{340+20}{340-20}\right) \\
& =324 \mathrm{~Hz}
\end{aligned}
$
