$A$ motorcycle starts from rest and accelerates along a straight path at $2 \; m/s^2$. At the starting point of the motorcycle,there is a stationary electric siren. How far has the motorcycle gone when the driver hears the frequency of the siren at $94 \%$ of its original value (in $; m$)? (Speed of sound $= 330 \; m/s$)

$A$ policeman on duty detects a drop of $10\%$ in the pitch of the horn of a moving car as it crosses him. If the velocity of sound is $330 \, m/s$,the speed of the car will be ..... $m/s$.

When the source of sound moves towards a stationary observer,the wavelength of sound received by him

$S_1$ and $S_2$ are two identical sound sources of frequency $656 \ Hz$. The source $S_1$ is located at $O$ and $S_2$ moves anti-clockwise with a uniform speed $4 \sqrt{2} \ ms^{-1}$ on a circular path around $O$,as shown in the figure. There are three points $P, Q$ and $R$ on this path such that $P$ and $R$ are diametrically opposite while $Q$ is equidistant from them. $A$ sound detector is placed at point $P$. The source $S_1$ can move along direction $OP$.
[Given: The speed of sound in air is $324 \ ms^{-1}$]
$(1)$ When only $S_2$ is emitting sound and it is at $Q$,the frequency of sound measured by the detector in $Hz$ is. . . . . .
$(2)$ Consider both sources emitting sound. When $S_2$ is at $R$ and $S_1$ approaches the detector with a speed $4 \ ms^{-1}$,the beat frequency measured by the detector is $\qquad$ $Hz$.

$A$ bus is moving with a velocity of $5 \, ms^{-1}$ towards a huge wall. The driver sounds a horn of frequency $165 \, Hz$. If the speed of sound in air is $335 \, ms^{-1}$, the number of beats heard per second by the passengers in the bus will be:

An observer moves towards a stationary source of sound with a velocity of one-fifth of the velocity of sound. The percentage increase in the apparent frequency is (in $\%$)