$A$ detector is released from rest over a source of sound of frequency $f_0 = 10^3 \, Hz$. The frequency observed by the detector at time $t$ is plotted in the graph. Given $g = 10 \, m/s^2$,find the speed of sound in air in $m/s$.

$A$ 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 $\,m$)

The observer is moving with velocity $v_0$ towards the stationary source of sound and then after crossing moves away from the source with velocity $v_0$. Assume that the medium through which the sound waves travel is at rest. If $v$ is the velocity of sound and $n$ is the frequency emitted by the source,then the difference between apparent frequencies heard by the observer is:

$A$ sound source is moving towards a stationary observer with $\frac{1}{10}$th the speed of sound. The ratio of apparent to real frequency is

$A$ person observes two moving trains. The first reaches the station and the second leaves the station,both with an equal speed of $30 \ m/s$. If both trains emit sounds of frequency $300 \ Hz$,what is the difference in frequencies heard by the person (in $Hz$)? (Speed of sound in air $= 330 \ m/s$)

$A$ car travelling at a speed of $54 \ km/h$ towards a wall sounds a horn of frequency $400 \ Hz$. The difference in the frequencies of two sounds, one received directly from the car and the other reflected from the wall, noticed by a person standing between the car and the wall is (speed of sound in air is $335 \ m/s$):