We’ve all observed how the sound of a car’s horn alters when it passes by at high speed: as each wave peak is emitted from a progressively nearer location, the wave gets tighter and the tone heightens. Conversely, as the vehicle moves away, the wave expands and the sound deepens. This fluctuation in sound frequency is the Doppler effect, which is applicable in various situations and significantly beneficial.
In a binary system, two stars are in a constant orbital dance. If the rotation plane is seen edge-on, one star is perceived as coming closer while the other drifts away. Assuming that both stars radiate similar light, the light from the star drawing nearer is blue-shifted, while the light from the drifting star red-shifts. Following a half-revolution, the stars swap positions, causing the colour shifts to invert. This phenomenon was elucidated by Christian Doppler in his 1842 work, “On the Coloured Light of the Binary Stars”.
Subsequently, the effect was confirmed for sound waves by the grandly named Dutch meteorologist, Christophorus Henricus Diedericus Buys Ballot. Best known for his law linking atmospheric pressure and wind direction – one version of which suggests that standing with your back to the wind and finding low pressure to your left signifies you’re in the northern hemisphere.
The Doppler effect has countless practical utilizations. Doppler radar, exceedingly useful in both civilian and military aviation, can ascertain the radial velocity of mobile targets. From a stationary vantage point, speed cameras and laser guns can detect traffic speed limit violations.
Puma technology enables mobile Garda vehicles to identify over-speeding drivers. Sonar technology makes use of sound waves rather than radio waves. The speed of water currents in rivers and oceans can be measured using a sonar current profiler which detects the Doppler effect in sound waves bounced off water particles. Sodar, an acronym for sound detection and ranging, operates on similar principles to measure wind speed.
Vascular Doppler ultrasonography plays a pivotal role in identifying irregularities in the body’s circulatory system. Not long ago, my carotid arteries were examined using an ultrasound scan, which facilitates the evaluation of blood flow in the carotid arteries. The velocity of the flow accelerates in spots where vascular constriction or obstruction occurs within an artery. The sonographic display portrays this visually in tones of red or blue, distinguishing the velocity and course of flow.
The Doppler frequency shift is an essential tool in the field of astronomy. Stars emit light in separate spectral lines, and the impact prompts slight yet perceptible shifts in these lines, as illustrated. This can inform us of the speed at which stars and galaxies are moving away or closer to us, separate close binary systems from solitary stars, and identify exoplanets that revolve around other stars.
Satellites move at a rapid pace, frequently altering their course, and the Doppler shift effect can be considerable. This necessitates a continuous adjustment of the transmission frequency. Weather radar is yet another platform where Doppler finds usage, where clouds as well as frontal systems are depicted in varied hues to signify their movements. This is indispensable for short-term weather prediction or nowcasting.
The relative frequency change betwixt the source and receiver is encapsulated by a straightforward mathematical formulation known as the Doppler equation. When the relative velocity surpasses the speed of sound, it results in a shock wave, triggering a sonic boom. In “The Theory of Sound,” a seminal text by English physicist Lord Rayleigh, he amusingly applies the Doppler equation, stating that an observer moving away from a musical source at double the speed of sound would hear the music at the right tempo and pitch but in reverse.
Peter Lynch, an emeritus professor at the School of Mathematics and Statistics at University College Dublin, authors a blog at thatsmaths.com.