$A$ source emitting sound of frequency $288 \,Hz$ is tied to a string of $100 \,cm$ length and rotated with an angular velocity of $20 \,rad/s$ in the horizontal plane. The range of frequencies heard by an observer standing at a distance of $5 \,m$ from the source is (in $Hz$) (Speed of sound in air $= 340 \,m/s$)

$A$ police car with a siren of frequency $8 \ kHz$ is moving with uniform velocity $36 \ km/h$ towards a tall building which reflects the sound waves. The speed of sound in air is $320 \ m/s$. The frequency of the siren heard by the car driver is (in $kHz$)

If a source emitting waves of frequency $F$ moves towards an observer with a velocity $V/3$ and the observer moves away from the source with a velocity $V/4$,the apparent frequency as heard by the observer will be ($V=$ velocity of sound).

$A$ source of sound $S$ in the form of a block kept on a smooth horizontal surface is connected to a spring, as shown in the figure. If the spring oscillates with an amplitude of $50 \,cm$ along the horizontal between the wall and the observer $O$, the maximum frequency heard by the observer is $12.5 \%$ more than the minimum frequency heard by him. If the mass of the source of sound is $100 \,g$, the force constant of the spring is (Speed of sound in air is $340 \,ms^{-1}$) (in $\,N m^{-1}$)

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 $kHz$)?

Consider two sound sources $S_1$ and $S_2$ having the same frequency $100\,Hz$ and the observer $O$ located between them as shown in the figure. All three are moving with the same velocity in the same direction. The beat frequency heard by the observer is .... $Hz$.