With what speed should a sound source move towards an observer so that the observer hears half the original frequency $(v)$?

Consider the Doppler effect in two cases. In the first case,an observer moves towards a stationary source of sound with a speed of $50 \,m/s$. In the second case,the observer is at rest and the source moves towards the observer with the same speed of $50 \,m/s$. Then the frequency heard by the observer will be [velocity of sound in air $= 330 \,m/s$.]

$A$ car sounding a horn of frequency $1000 \text{ Hz}$ passes an observer. The ratio of frequencies noted by the observer before and after the car passes is $11:9$. If the speed of sound is $V$,what is the speed of the car?

$A$ stationary source emits sound of frequency $f_0 = 492 \,Hz$. The sound is reflected by a large car approaching the source with a speed of $v_c = 2 \,ms^{-1}$. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in $Hz$? (Given that the speed of sound in air is $v = 330 \,ms^{-1}$ and the car reflects the sound at the frequency it has received).

Suppose that the speed of sound in air at a given temperature is $400 \ m/s$. An engine blows a whistle at $1200 \ Hz$ frequency. It is approaching an observer at the speed of $100 \ m/s$. What is the apparent frequency as heard by the observer in $Hz$?

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 .... $Hz$.