$A$ source of sound whose frequency is $1000 \text{ Hz}$ is moving with a speed of $33 \text{ m/s}$. The waves reflected by a fixed obstacle are registered by a receiver that moves together with the source. If the speed of the sound waves is $330 \text{ m/s}$, then the frequency registered by the receiver is: (in $\text{ kHz}$)

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $1.0 \ m \ s^{-1}$ and the man behind walks at a speed $2.0 \ m \ s^{-1}$. $A$ third man is standing at a height $12 \ m$ above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency $1430 \ Hz$. The speed of sound in air is $330 \ m \ s^{-1}$. At the instant when the moving men are $10 \ m$ apart,the stationary man is equidistant from them. The frequency of beats in $Hz$ heard by the stationary man at this instant is:

When the source of sound moves towards a stationary observer,the wavelength of sound received by him

$A$ source of sound of frequency $640 \,Hz$ is moving at a velocity of $\frac{100}{3} \,m/s$ along a road, and is at an instant $30 \,m$ away from a point $A$ on the road. $A$ person standing at $O$, $40 \,m$ away from the road, hears sound of apparent frequency $v^{\prime}$. The value of $v^{\prime}$ is (velocity of sound $= 340 \,m/s$): (in $\,Hz$)

Two sources of sound $S_1$ and $S_2$ are moving towards and away from a stationary observer with the same speed $V$ respectively. The observer detects $3$ beats per second. Find the speed of the source (approximately) in $m/s$. Given: $f_1 = f_2 = 500 \, Hz$,speed of sound in air $= 330 \, m/s$.

$A$ source of sound is moving with a constant velocity of $30 \,m/s$ emitting a note of frequency $256 \,Hz$. The ratio of frequencies observed by a stationary observer while the source is approaching him and after it crosses him is [speed of sound in air $= 330 \,m/s$].