A passing siren can seem to fall in pitch just as the vehicle goes by. Even if the source holds one steady tone, a listener ahead of it receives wave cycles more frequently than a listener behind it. This change in received frequency is the Doppler effect. It is separate from the sound getting louder as the vehicle comes closer.
The source moves between one wave and the next
Imagine a siren emitting regularly spaced pressure pulses. After one pulse leaves, it travels through the air. Before the next pulse is emitted, the vehicle has moved forward. Ahead of the vehicle, successive pulses are packed into a shorter distance. Behind it, they are spread farther apart.
In still air, the sound’s speed relative to the air is set mainly by the air’s conditions, not by adding the vehicle’s speed. Shorter spacing means more wave cycles reach a stationary listener each second, so the pitch is higher. Wider spacing means fewer cycles per second and a lower pitch. OpenStax explains the moving-source and moving-listener cases.
A paper model you can make at a desk
Draw a straight line and place four equally spaced dots on it, labeled 1 through 4. These are the source’s positions at successive instants. At the fourth instant, the oldest wave has traveled farthest: draw a large circle around dot 1, a smaller circle around dot 2 and a smaller one again around dot 3. Use the same reduction in radius each time, larger than the spacing between adjacent dots.
Now compare the gaps between the circles ahead of dot 4 with those behind dot 1. The front gaps are smaller. You have drawn a snapshot of waves emitted at different places, not waves physically pushed along by a vehicle. For comparison, redraw the circles around one common center. That second picture represents a stationary source.
How large can the shift be?
For a stationary listener and a source traveling directly toward them in still air, the received frequency equals the source frequency multiplied by c ÷ (c − v). Here c is the speed of sound and v is the source speed. For motion directly away, replace the minus sign with a plus sign.
As an idealized example, take a steady 500-hertz tone, a source speed of 20 meters per second and a sound speed of 343 meters per second. Approaching, the calculation is 500 × 343 ÷ 323, or about 531 hertz. Receding, it is 500 × 343 ÷ 363, or about 472 hertz. These are calculated values for those assumptions, not measurements of a real siren. OpenStax’s Doppler chapter gives the underlying relationships.
Why real pass-bys sound more complicated
A vehicle on a road does not normally travel directly into a listener. During a pass-by, its direction relative to the listener changes, so the received pitch changes through the encounter rather than jumping between two perfectly flat notes. A closer pass can make that transition seem more abrupt.
Real emergency sirens also change their emitted pitch deliberately. Engine speed can change, and buildings can send reflected sound toward you along different paths. A phone recording may include all of those effects. Listen to an educational recording at a comfortable volume rather than approaching a road or railway to collect one.
Three things to keep separate
Pitch is related to the rate of wave cycles reaching you. Loudness concerns the strength and perception of the sound. Timbre concerns its character and frequency mixture. A sound can become quieter without changing pitch, or change pitch without its source becoming quieter. The Doppler effect concerns the first of these distinctions, not every change you notice in a passing vehicle.
For another example of sound traveling through air, read what causes thunder. Thunder’s delay and rumble raise different questions from a moving siren’s pitch shift.
Optional equipment to explore
Paper and a pencil are enough for the wavefront model. For further study, browse introductory acoustics books or classroom wave-demonstration springs on Amazon. These are search links, not tested recommendations. A spring illustrates wave motion but does not automatically reproduce a moving-source Doppler experiment.
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