$A$ source of sound emitting a note of frequency $200 Hz$ moves towards an observer with a velocity $v$ equal to the velocity of sound. If the observer also moves away from the source with the same velocity $v$,the apparent frequency heard by the observer is .... $Hz$

$A$ car moving towards a wall at a velocity of $30 \, m/s$ sounds a horn of frequency $600 \, Hz$. What frequency $(Hz)$ will the driver hear? (Speed of sound in air = $330 \, m/s$)

The wavelength is $120 \, cm$ when the source is stationary. If the source is moving with a relative velocity of $60 \, m/s$ towards the observer,then the wavelength of the sound wave reaching the observer will be ... $cm$ (velocity of sound $= 330 \, m/s$).

$A$ source of sound of frequency $500 Hz$ is moving towards an observer with velocity $30 m/s$. The speed of sound is $330 m/s$. The frequency heard by the observer will be .... $Hz$

An obstacle is moving towards the source with velocity $v$. The sound is reflected from the obstacle. If $c$ is the speed of sound and $\lambda$ is the wavelength,then the wavelength of the reflected wave $(\lambda_{r})$ is

$S_1$ 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 $\qquad$ $Hz$.