$A$ motor-cyclist moving towards a huge cliff with a speed of $18 \ kmh^{-1}$,blows a horn of source frequency $325 \ Hz$. If the speed of the sound in air is $330 \ ms^{-1}$,the number of beats heard by him is

An observer moves towards a stationary source of sound with a speed $\frac{1}{5}^{\text{th}}$ of the speed of sound. The wavelength and frequency of the waves emitted by the source are $\lambda$ and $f$ respectively. The apparent frequency and wavelength heard by the observer are respectively,

$A$ racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If $v$ is the velocity of sound,the velocity of the car will be

$A$ stationary source emits sound of frequency $f_0 = 492 \,Hz$. The sound is reflected by a large car approaching the source with a speed of $v_c = 2 \,ms^{-1}$. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in $Hz$? (Given that the speed of sound in air is $v = 330 \,ms^{-1}$ and the car reflects the sound at the frequency it has received).

$A$ 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 $m/s$)

$A$ train is moving towards a stationary observer with speed $34 \text{ m/s}$. $A$ train sounds a whistle of frequency $450 \text{ Hz}$. If the speed of sound is $340 \text{ m/s}$, the frequency heard by the observer in Hz is