$A$ car sounding a horn of frequency $1200 \text{ Hz}$ passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is $7:5$. If the speed of sound is $V$,the speed of the car is:

An engine is moving on a circular path of radius $200 \,m$ with a speed of $15 \,m/s$. What will be the frequency heard by an observer who is at rest at the centre of the circular path,when the engine blows the whistle with a frequency of $250 \,Hz$?

$A$ man sitting in a moving train hears the whistle of the engine. The frequency of the whistle is $600 \ Hz$.

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 $kHz$)?

$A$ source $(S)$ of sound has a frequency of $240 \ Hz$. When the observer $(O)$ and the source move towards each other at a speed $v$ with respect to the ground (as shown in Case $1$ in the figure),the observer measures the frequency of the sound to be $288 \ Hz$. However,when the observer and the source move away from each other at the same speed $v$ with respect to the ground (as shown in Case $2$ in the figure),the observer measures the frequency of the sound to be $n \ Hz$. The value of $n$ is:

$A$ police car moving at $22 \,ms^{-1}$ chases a motorcyclist. The policeman sounds a horn at $176 \,Hz$, while both of them move towards a stationary siren of frequency $165 \,Hz$. If the number of beats heard by the motorcyclist per second is zero, then the speed of the motorcycle is (Speed of sound in air $= 330 \,ms^{-1}$) (in $\,ms^{-1}$)