Three musicians experiment with the Doppler effect. Musician $A$ rides in a car at a speed $u$ directly away from musician $B$ who is stationary. Musician $C$ rides in a car directly toward $B$ and travels at the same speed as $A$. Musician $A$ plays a note at frequency $f_A$ on his trumpet. $B$ hears the note,adjusts his trumpet,and plays the same note he heard. Choose the incorrect statement.

Which pre-assumptions are used for the Doppler effect?

An engine moving towards a wall with a velocity $50 \ m/s$ emits a note of $1.2 \ kHz$. The speed of sound in air is $350 \ m/s$. The frequency of the note after reflection from the wall as heard by the driver of the engine is: (in $kHz$)

The observer is moving with velocity $v_0$ towards the stationary source of sound and then after crossing moves away from the source with velocity $v_0$. Assume that the medium through which the sound waves travel is at rest. If $v$ is the velocity of sound and $n$ is the frequency emitted by the source,then the difference between apparent frequencies heard by the observer is:

Two loudspeakers $M$ and $N$ are located $20 \ m$ apart and emit sound at frequencies $118 \ Hz$ and $121 \ Hz$,respectively. $A$ car is initially at a point $P$,$1800 \ m$ away from the midpoint $Q$ of the line $MN$ and moves towards $Q$ constantly at $60 \ km/h$ along the perpendicular bisector of $MN$. It crosses $Q$ and eventually reaches a point $R$,$1800 \ m$ away from $Q$. Let $v(t)$ represent the beat frequency measured by a person sitting in the car at time $t$. Let $v_P, v_Q$ and $v_R$ be the beat frequencies measured at locations $P, Q$ and $R$,respectively. The speed of sound in air is $330 \ m/s$. Which of the following statement$(s)$ is(are) true regarding the sound heard by the person?
$(A)$ $v_P + v_R = 2v_Q$
$(B)$ The rate of change in beat frequency is maximum when the car passes through $Q$
$(C)$ The plot below represents schematically the variation of beat frequency with time (Left plot)
$(D)$ The plot below represents schematically the variation of beat frequency with time (Right plot)

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