$A$ student holds a tuning fork oscillating at $170 \,Hz$. He walks towards a wall at a constant speed of $2 \,ms^{-1}$. The beat frequency observed by the student between the tuning fork and its echo is (Velocity of sound $=340 \,ms^{-1}$ ) (in $\,Hz$)

An audio transmitter $(T)$ and a receiver $(R)$ are hung vertically from two identical massless strings of length $8 \ m$ with their pivots well separated along the $X$ axis. They are pulled from the equilibrium position in opposite directions along the $X$ axis by a small angular amplitude $\theta_0 = \cos^{-1}(0.9)$ and released simultaneously. If the natural frequency of the transmitter is $660 \ Hz$ and the speed of sound in air is $330 \ m/s$,the maximum variation in the frequency (in $Hz$) as measured by the receiver (Take the acceleration due to gravity $g = 10 \ m/s^2$) is:

Two sources of sound of same frequency are placed at a distance of $100\,m$ from each other. An observer moving in between them hears $4$ beats per second. If the distance between the sound sources is increased to $400\,m$,then the number of beats heard by him will be:

$A$ source of sound $S$ emitting waves of frequency $100 \, Hz$ and an observer $O$ are located at some distance from each other. The source is moving with a speed of $19.4 \, m s^{-1}$ at an angle of $60^{\circ}$ with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer is .... $Hz$ (velocity of sound in air $330 \, m s^{-1}$).

An observer moves towards a stationary source of sound, with a speed of one-fifth of the speed of sound. The apparent increase in the frequency heard by the observer is (in $\%$)

An engine giving a whistle is moving towards a stationary observer with a speed of $110\, m/s$. What will be the ratio of the frequency of the whistle heard when the engine is approaching and receding from the observer? (Speed of sound $= 330\, m/s$)