The motion of the train causes these changes in wavelength and frequency. To
understand this, consider two successive regions of condensation generated by the
train’s horn. The first moves toward the listener. The train continues to move forward,
and the next time the horn creates a region of condensation, it will be closer to the prior
one than if the train were stationary. The regions arrive more frequently because of the
motion of the train toward the listener.
Concept 3 shows the effect perceived by a listener for whom the train is moving away.
The sound waves reach this listener less frequently, and he hears a lower pitched
sound.
The Doppler effect is quantified using the two equations shown to the right. (They apply
when the sound source is moving; a different set of equations is used when the listener
is moving.) The first equation shows how to calculate the frequency when the source of
the sound moves directly toward a stationary listener; the second is used when the
source moves directly away. If the source is moving in some other direction, the
component of its velocity directly toward or away from the listener must be used in the
formulas. The speed of sound changes with temperature, air density and so on; a value
of 343 m/s is often used.
Source moves toward listener
Sound wavefronts arrive closer together
Listener hears higher frequencySource moves away from
listener
Sound wavefronts arrive farther apart
Listener hears lower frequency