$A$ siren emitting sound of frequency $500 \; Hz$ is going away from a static listener with a speed of $50 \; m/s$. The frequency of sound heard by the listener is .... $Hz$. (Take speed of sound $v = 330 \; m/s$)

$A$ speaker emits a sound wave of frequency $f_0$. When it moves towards a stationary observer with speed $u$,the observer measures a frequency $f_1$. If the speaker is stationary and the observer moves towards it with speed $u$,the measured frequency is $f_2$. Then,

$A$ vehicle with a horn of frequency $n$ is moving with a velocity of $30\, m/s$ in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency $n + n_1$. Then (if the sound velocity in air is $300\, m/s$):

With what velocity an observer should move relative to a stationary source so that a sound of double the frequency of the source is heard by the observer?

When an 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 stationary source with velocity $V_1$,the apparent frequency is $F_2$. If $v$ is the velocity of sound in air and $\frac{F_1}{F_2} = 2$,then $\frac{v}{V_1}$ is equal to:

$A$ whistle of frequency $540 Hz$ rotates in a horizontal circle of radius $2 m$ at an angular speed of $15 rad/s$. What is the highest frequency heard by a listener at rest with respect to the center of the circle (in $Hz$)? (Velocity of sound in air $= 330 m/s$)