$A$ source of sound of frequency $90 \text{ vibrations/sec}$ is approaching a stationary observer with a speed equal to $1/10$ the speed of sound. What will be the frequency heard by the observer in $\text{vibrations/sec}$?

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be $\dots \;$%.

$A$ source $S$ emitting sound of frequency $288 \,Hz$ is fixed on block $B$ which is attached to the free end of a spring $S_2$, and an observer $O$ is on block $A$ which is attached to the free end of spring $S_1$ as shown in the figure. The blocks $A$ and $B$ are simultaneously displaced towards each other through a distance of $0.5 \,m$ and then left to oscillate. If the angular velocity of each block is $40 \,rad/s$, then the maximum frequency observed by the observer is (speed of sound in air is $340 \,m/s$): (in $\,Hz$)

$A$ stationary source is emitting sound at a fixed frequency $f_0$,which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is $1.2 \%$ of $f_0$. What is the difference in the speeds of the cars (in $km/h$) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound,which is $330 \ m/s$.

$A$ train standing at the outer signal of a railway station blows a whistle of frequency $400 \ Hz$ in still air. The train begins to move with a speed of $10 \ ms^{-1}$ towards the platform. What is the frequency of the sound for an observer standing on the platform (in $Hz$)? (Sound velocity in air $= 330 \ ms^{-1}$).

$A$ siren placed at a railway platform is emitting sound of frequency $5 \text{ kHz}$. $A$ passenger sitting in a moving train $A$ records a frequency of $5.5 \text{ kHz}$ while the train approaches the siren. During his return journey in a different train $B$,he records a frequency of $6.0 \text{ kHz}$ while approaching the same siren. The ratio of the velocity of train $B$ to that of train $A$ is