Two sources $A$ and $B$ are sounding notes of frequency $660 \, Hz$. $A$ listener moves from $A$ to $B$ with a constant velocity $u$. If the speed of sound is $330 \, m/s$,what must be the value of $u$ so that he hears $8$ beats per second?

$A$ car moves towards a hill with speed $v_c$. It blows a horn of frequency $f$ which is heard by an observer following the car with speed $v_o$. The speed of sound in air is $v$.

$A$ whistle sends out $256$ waves in a second. If the whistle approaches the observer with a velocity equal to $\frac{1}{3}$ of the velocity of sound in air,calculate the number of waves per second the observer will receive.

Obtain the equation for the frequency observed by a stationary observer when the source is moving.

$A$ motorcycle starts from rest from a stationary source of sound and moves away from the source with a uniform acceleration $2 \,m/s^2$. The distance travelled by the motorcycle when the person on it hears the sound of frequency which is $94 \%$ of the true frequency is nearly (speed of sound in air $= 330 \,m/s$): (in $\,m$)

$A$ train moving at a speed of $220\, m s^{-1}$ towards a stationary object,emits a sound of frequency $1000\, Hz$. Some of the sound reaching the object gets reflected back to the train as an echo. The frequency of the echo as detected by the driver of the train is ...... $Hz$. (Speed of sound in air is $330\, m s^{-1}$)