$A$ police car moving at $22 \ m/s$ chases a motorcyclist. The policeman sounds his horn at $176 \ Hz$,while both of them move towards a stationary siren of frequency $165 \ Hz$. Calculate the speed of the motorcycle,if it is given that he does not observe any beats. (in $m/s$)

Which of the following statements is false?

$A$ sound source is moving on a circular path of radius $R$ with constant angular speed $\omega$ in an anticlockwise direction and emits a frequency $n$. An observer performs simple harmonic motion along the path $QPR$ with time period $T = \frac{2\pi}{\omega}$ as shown in the figure. If at $t = 0$ the source is at $A$ and the observer is at $Q$,and assuming $OP$ is very large compared to the radius $R$ and $QP$,then:

$A$ whistle emitting a loud sound of frequency $540 \,Hz$ is whirled in a horizontal circle of radius $2 \,m$ at a constant angular speed of $15 \,rad/s$. The speed of sound is $330 \,m/s$. The ratio of the highest to the lowest frequency heard by a listener standing at rest at a large distance from the centre of the circle is

$A$ siren emitting sound of frequency $500 \; Hz$ is going away from a static listener with a speed of $50 \; m/s$. The frequency of sound heard by the listener is .... $Hz$. (Take speed of sound $v = 330 \; m/s$)

When a car is approaching the observer,the frequency of the horn is $100 \, Hz$. After passing the observer,it is $50 \, Hz$. If the observer moves with the car,the frequency will be $\frac{x}{3} \, Hz$ where $x = .....$