When the observer moves towards a stationary source with velocity $V_1$,the apparent frequency of the emitted note is $F_1$. When the observer moves away from the source with velocity $V_1$,the apparent frequency is $F_2$. If $V$ is the velocity of sound in air and $F_1 / F_2 = 2$,then $V / V_1$ is equal to:

$A$ sound source is tied to one end of a string of length $50 \ cm$ and is rotated with an angular speed of $40 \ rad \ s^{-1}$ in a horizontal plane. The ratio of the maximum and minimum frequencies of the sound heard by an observer standing at a distance of $10 \ m$ from the fixed end of the string is (speed of sound in air $= 340 \ m \ s^{-1}$).

$A$ source is moving towards an observer with a speed of $20 \ m/s$ and having a frequency of $240 \ Hz$. The observer is now moving towards the source with a speed of $20 \ m/s$. If the velocity of sound is $340 \ m/s$,the apparent frequency heard by the observer is ... $Hz$.

$A$ bat is flitting about in a cave,navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is $40\; kHz$. During one fast swoop directly toward a flat wall surface,the bat is moving at $0.03$ times the speed of sound in air. What frequency (in $kHz$) does the bat hear reflected off the wall?

When both source and listener are approaching each other,the observed frequency of sound is given by (where $V$ is the speed of sound,$V_L$ and $V_S$ are the velocities of the listener and source respectively,and $n_0$ is the radiated frequency):

$A$ source,approaching with speed $u$ towards the open end of a stationary pipe of length $L$,is emitting a sound of frequency $f_s$. The farther end of the pipe is closed. The speed of sound in air is $v$ and $f_0$ is the fundamental frequency of the pipe. For which of the following combination$(s)$ of $u$ and $f_s$,will the sound reaching the pipe lead to a resonance?
$(A)$ $u=0.8 v$ and $f_s=f_0$
$(B)$ $u=0.8 v$ and $f_s=2 f_0$
$(C)$ $u=0.8 v$ and $f_s=0.5 f_0$
$(D)$ $u=0.5 v$ and $f_s=1.5 f_0$