Why does a Fire truck siren change pitch when it passes us?
Asked by: Patrick Knight
The pitch of the siren of a Fire truck appears to change as the truck passes us due to the Doppler effect. Of course, to an observer on the truck, the pitch does not change at all.
Since the speed of sound in air is essentially fixed, the perceived pitch of a tone is related to the wavelength of the sound. The shorter the wavelength, the higher the pitch, and vice-versa. The wavelength can be conveniently considered to be the distance between successive 'crests' of the waves of pressure that constitute the sound wave.
Consider a tone emitted in the forward direction in which the Fire truck is moving and consider the launching of two successive wave crests. The first crest is launched and travels in the (assumed still) air at the speed of sound (relative to the air). If the truck were not moving, the second crest would be launched after the first had travelled one wavelength. However, because the truck is moving in the same direction as the sound, the distance between the first crest and the second, at the time the second is launched, is less than previously. That is, the wavelength between successive crests is decreased due to the motion of the truck in the same direction as the sound. Since the wavelength is decreased, but the speed of the sound in the air is unaltered (it is determined by the properties of the air and is unaffected by the motion of the source of the sound on the truck), the pitch of the sound is increased in the direction in which the truck is moving.
Conversely, the wavelength between crests of sound waves launched in the direction opposite to the direction in which the Fire truck is moving will be increased. The forward motion of the truck adds extra distance between the crests, increasing the wavelength and, consequently, decreasing the pitch of the sound in the direction away from which the truck is moving.
The tendency to increase or decrease the wavelength of the sound due to the motion of the source is called the Doppler effect.
Hence, when the Fire truck is coming toward you, the wavelength is decreased and the pitch is above the pitch when the source is at rest. When the truck passes and is moving away from you, the opposite holds true. The wavelength is increased and the pitch is decreased below the value when the source is at rest. The result is the familiar change of pitch from high to low as the Fire truck passes.
Answered by: Warren Davis, Ph.D., President, Davis Associates, Inc., Newton, MA USA
'A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.'