A source of sound moves along the X-axis at a speed of 22 m s^ -1 ,...

The sound received by the listener was emitted when the source was at the origin $P$.

At this instant, the velocity of the source is directed along the X-axis, while the line joining the source to the listener lies along the Y-axis.

The angle $\theta$ between the velocity vector of the source and the line of sight from the source to the listener is $90^\circ$.

The apparent frequency $f'$ heard by the listener is given by the Doppler effect formula:

f' = f \left(\dfrac{v}{v - v_s \cos \theta} \right)

where $v$ is the speed of sound and $v_s$ is the speed of the source.

Substituting $\theta = 90^\circ$, we get $\cos 90^\circ = 0$:

f' = f \left(\dfrac{v}{v - 0} \right) =$f$

Given the original frequency $f = 2.0 \text{ kHz}$, the frequency heard by the listener is:

$f' = 2.0 \text{ kHz}$