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?

$A$ 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

$A$ train blowing its whistle moves with constant speed on a straight track towards an observer and then crosses him. If the ratio of the difference between the actual and apparent frequencies is $3:2$ in the two cases (approaching and receding),then the speed of the train is (where $v$ is the speed of sound).

An Indian submarine $(I)$ and an enemy submarine $(E)$ move towards each other in motionless water. The Indian submarine moves at $50 \ km/h$,and the enemy submarine at $70 \ km/h$. The Indian submarine sends out a sonar signal (sound wave in water) at $1000 \ Hz$. The sonar wave reflects off the enemy submarine and returns to the Indian submarine. If the speed of sound in water is $5500 \ km/h$,what is the frequency of the reflected signal detected by the Indian submarine in $kHz$ (in $kHz$)?

$A$ train whistling at a constant frequency $n_0$ is moving towards a station at a constant speed $v$. The train passes a stationary observer on the station. The frequency $n$ of the sound as heard by the observer is plotted as a function of time $t$. Identify the expected curve.

An engine is moving on a circular track with a constant speed. It is blowing a whistle of frequency $500 \ Hz$. The frequency received by an observer standing stationary at the centre of the track is