$A$ police car moving at $22 \,ms^{-1}$ chases a motorcyclist. The policeman sounds a horn at $176 \,Hz$, while both of them move towards a stationary siren of frequency $165 \,Hz$. If the number of beats heard by the motorcyclist per second is zero, then the speed of the motorcycle is (Speed of sound in air $= 330 \,ms^{-1}$) (in $\,ms^{-1}$)

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

$A$ source and a listener are both moving towards each other with a speed of $\frac{V}{10}$ (where $V$ is the speed of sound). If the frequency of the sound note emitted by the source is $n$,then the frequency heard by the listener would be nearly:

An observer and a source emitting sound of frequency $120 \,Hz$ are on the $X$-axis. The observer is stationary while the source of sound is in motion given by the equation $x=3 \sin \omega t$ (where $x$ is in metres and $t$ is in seconds). If the difference between the maximum and minimum frequencies of the sound observed by the observer is $22 \,Hz$,then the value of $\omega$ is (speed of sound in air $=330 \,ms^{-1}$):

$A$ source of sound emits sound waves at frequency $f_0$. It is moving towards an observer with fixed speed $v_s$ ($v_s < v$,where $v$ is the speed of sound in air). If the observer were to move towards the source with speed $v_0$,the variation of the frequency $f$ heard by the observer as $v_0$ is changed is given by one of the following two graphs ($A$ and $B$). The variation of $f$ with $v_0$ is given correctly by:

$A$ source and an observer both start moving simultaneously from the origin,one along the $x-$axis and the other along the $y-$axis,with the speed of the source being twice the speed of the observer. The graph between the apparent frequency $f$ observed by the observer and time $t$ would approximately be: