What Is the Doppler Effect? Why a Siren Drops as It Passes

A stationary source emits waves that spread outward as evenly spaced spheres, and a listener in any direction receives crests at exactly the rate the source produced them. Set the source moving and it travels a little way toward the next crest before emitting it, so in front of the source the crests bunch up and behind it they stretch out. Wavelength and frequency are inversely related, so bunched crests mean a shorter wavelength and a higher perceived pitch, and stretched crests mean the opposite. The speed of the wave through the air is unchanged throughout, which is the point people usually miss: the source is not throwing sound faster, it is spacing the crests differently. The effect is identical if the listener moves instead of the source, with a small difference in the exact formula when the medium itself is involved.

The abrupt change as a vehicle passes is worth explaining because it is not a gradual glide. What matters is the component of velocity directly toward or away from you, which is called the radial velocity, and a vehicle passing on a road is moving almost entirely toward you as it approaches, then almost entirely across your line of sight at the closest point, then almost entirely away. The transition through that sideways moment happens quickly, which is why the pitch seems to fall abruptly at the instant of passing. If the same vehicle were driving directly at you and then swerved, the change would be different, and if it drove in a circle around you at constant radius there would be no shift at all, because nothing about the distance is changing.

The effect is a measuring instrument wherever a relative velocity needs to be known without touching anything:

• •Radar speed guns bounce microwaves off a vehicle and measure the frequency shift of the return, which gives the speed directly
• •Weather radar uses the shift to see not just where rain is but which way it is moving, which is what makes rotation inside a storm visible and is the basis of tornado warning
• •Medical ultrasound measures blood flow by the shift from moving red cells, which shows the direction and speed of flow in an artery and detects narrowing or clots
• •Astronomers measure the radial velocity of stars, which reveals binary companions, orbiting planets and the rotation of galaxies
• •Sonar and fish finders use it, as do bats, which adjust their call frequency in flight to compensate for their own motion and keep the echoes in the range their ears are tuned to
• •Satellite navigation uses it in reverse, since the shift in a satellite's signal helps determine a receiver's motion

Light behaves the same way with two differences that matter. Because light needs no medium, only the relative velocity of source and observer counts, and relativity must be included, which adds a term for time dilation and produces a transverse effect even for motion exactly across the line of sight. In astronomy the shift is measured by the position of spectral lines, the sharp dark or bright features produced by particular elements, whose rest wavelengths are known precisely from laboratory work. A source moving away has its lines shifted toward longer wavelengths, which is redshift, and one approaching shows blueshift. Hubble's measurement that almost all galaxies are redshifted, and by an amount proportional to their distance, is the observational basis for the expanding universe. The same technique detects exoplanets, since a star with a planet wobbles slightly about the common centre of mass and its lines shift back and forth by a few metres per second, a precision that modern spectrographs achieve routinely.

Two refinements are worth having. Cosmological redshift is not strictly a Doppler shift, because distant galaxies are not moving through space away from us so much as the space between us is expanding, stretching the light in transit. The formula looks similar at small distances and diverges at large ones, which is why it is possible for very distant galaxies to have recession speeds exceeding light without violating relativity, since nothing is moving through space at that rate. At the other end, when a source reaches the speed of the waves it is emitting, the crests in front cannot get ahead of it and pile up into a single shock front, which is a sonic boom in air, and the conical wake behind is the same geometry as a boat's bow wave in water. Christian Doppler proposed the effect in 1842 to explain the colours of binary stars, which was the wrong application, and it was tested for sound three years later by a Dutch scientist who put a band of trumpeters on an open railway carriage and had musicians on the platform record what they heard.

The effect arises because a moving source bunches its wave crests ahead of it and stretches them behind, raising the received frequency on approach and lowering it on departure, while the wave itself travels at a constant speed. Only motion directly toward or away counts, which is why the pitch drops sharply at the moment of passing. The same principle measures vehicle speed, storm rotation and blood flow, and in light it detects orbiting exoplanets and provided the evidence for an expanding universe, though cosmological redshift is a stretching of space rather than true motion.