When an ambulance approaches an observer, the sound of the siren perceived during the approach is more acute (greater frequency) than the sound perceived when the ambulance moves away, which is a more bass sound (decrease in frequency). In these situations, the apparent frequency \(f'\), which is perceived by the observer, does not coincide with the frequency \(f\) of the source. This phenomenon is known as Doppler effect .

Doppler effect . The figure illustrates two sources (speakers) emitting waves (sound). When the source is stopped, figure on the left, the sound propagates equally in all directions. When the source moves, figure on the right, the wave events arrive faster and faster in one direction and slower and slower in another. Therefore, depending on the position, the frequency will be different.

Relationship Between \(f'\) and \(f\)

The frequency \(f\), emitted by a source that moves with velocity \(v_{source}\), will be perceived by an observer moving with velocity \(v_{obs}\), according to the following ratio: $$ f' = f \frac{v_{sound} \pm v_{obs}}{v_{sound} \pm v_{source}},$$ where the signs (+) or (-) to \(v_{obs}\) and \(v_{source}\) should be chosen as follows.

\(v_{obs}\) :
(+) \(\rightarrow\) Moving towards the source
(-) \(\rightarrow\) Moving in the opposite direction of the source
\(v_{source}\) :
(-) \(\rightarrow\) Moving towards the observer
(+) \(\rightarrow\) Moving in the opposite direction of the observer

Note that the signal selection logic is reversed!