$A$ car is moving towards a high cliff. The car driver sounds a horn of frequency $f$. The reflected sound heard by the driver has a frequency $2f$. If $v$ is the velocity of sound,then the velocity of the car,in the same velocity units,will be:

$A$ source,approaching with speed $u$ towards the open end of a stationary pipe of length $L$,is emitting a sound of frequency $f_s$. The farther end of the pipe is closed. The speed of sound in air is $v$ and $f_0$ is the fundamental frequency of the pipe. For which of the following combination$(s)$ of $u$ and $f_s$,will the sound reaching the pipe lead to a resonance?
$(A)$ $u=0.8 v$ and $f_s=f_0$
$(B)$ $u=0.8 v$ and $f_s=2 f_0$
$(C)$ $u=0.8 v$ and $f_s=0.5 f_0$
$(D)$ $u=0.5 v$ and $f_s=1.5 f_0$

$A$ source is moving towards an observer with a speed of $20 \ m/s$ and having a frequency of $240 \ Hz$. The observer is now moving towards the source with a speed of $20 \ m/s$. If the velocity of sound is $340 \ m/s$,the apparent frequency heard by the observer is ... $Hz$.

$A$ siren emitting sound of frequency $800 \; Hz$ is going away from a static listener with a speed of $30 \; m/s$. The frequency of the sound heard by the listener is... $Hz$ (take velocity of sound as $330 \; m/s$).

$A$ train is moving with a uniform speed $33 \ m/s$ and an observer is approaching the train with the same speed. If the train blows a whistle of frequency $1000 \ Hz$ and the velocity of sound is $333 \ m/s$, then the apparent frequency of the sound that the observer hears is: (in $Hz$)

Two stationary sources each emit waves of wavelength $\lambda$. An observer moves from one source to the other with velocity $u$. The number of beats heard by the observer is: