$A$ source of sound is moving with a velocity of $50 \ m/s$ towards a stationary observer. The observer measures the frequency of sound as $500 \ Hz$. The apparent frequency of sound as heard by the observer when the source is moving away from him with the same speed is (Speed of sound at room temperature $350 \ m/s$). (in $Hz$)

$A$ 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 $v$.

$A$ and $B$ are two sources generating sound waves. $A$ listener is situated at $C$. The frequency of the source at $A$ is $500 \, Hz$. $A$ now moves towards $C$ with a speed of $4 \, m/s$. The number of beats heard at $C$ is $6$. When $A$ moves away from $C$ with a speed of $4 \, m/s$,the number of beats heard at $C$ is $18$. The speed of sound is $340 \, m/s$. The frequency of the source at $B$ is ..... $Hz$.

$A$ train $S_1$,moving with a uniform velocity of $108 \ km/h$,approaches another train $S_2$ standing on a platform. An observer $O$ moves with a uniform velocity of $36 \ km/h$ towards $S_2$,as shown in the figure. Both the trains are blowing whistles of the same frequency $120 \ Hz$. When $O$ is $600 \ m$ away from $S_2$ and the distance between $S_1$ and $S_2$ is $800 \ m$,the number of beats heard by $O$ is: [Speed of sound $= 330 \ m/s$]

$A$ motorcycle starts from rest and accelerates along a straight path at $2 \; m/s^2$. At the starting point of the motorcycle,there is a stationary electric siren. How far has the motorcycle gone when the driver hears the frequency of the siren at $94 \%$ of its original value (in $; m$)? (Speed of sound $= 330 \; m/s$)

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