Smile of the Day Tuesday, May 25, 2021

Tuesday May 25, 2021’s Smile of the Day: Doppler Effect

On this Day:

In 1842, Christian Doppler presented his idea, now known as the Doppler Effect, to the Royal Bohemian Society, Prague.

The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842.

A common example of Doppler shift is the change of pitch heard when a vehicle sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession.

The reason for the Doppler effect is that when the source of the waves is moving towards the observer, each successive wave crest is emitted from a position closer to the observer than the crest of the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrivals of successive wave crests at the observer is reduced, causing an increase in the frequency. While they are traveling, the distance between successive wave fronts is reduced, so the waves “bunch together”. Conversely, if the source of waves is moving away from the observer, each wave is emitted from a position farther from the observer than the previous wave, so the arrival time between successive waves is increased, reducing the frequency. The distance between successive wave fronts is then increased, so the waves “spread out”.

For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analyzed separately. For waves which do not require a medium, such as electromagnetic waves or gravitational waves, only the relative difference in velocity between the observer and the source needs to be considered, giving rise to the relativistic Doppler effect.

Doppler first proposed this effect in 1842 in his treatise “Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels” (On the coloured light of the binary stars and some other stars of the heavens). The hypothesis was tested for sound waves by Buys Ballot in 1845. He confirmed that the sound’s pitch was higher than the emitted frequency when the sound source approached him, and lower than the emitted frequency when the sound source receded from him. Hippolyte Fizeau discovered independently the same phenomenon on electromagnetic waves in 1848 (in France, the effect is sometimes called “effet Doppler-Fizeau” but that name was not adopted by the rest of the world as Fizeau’s discovery was six years after Doppler’s proposal). In Britain, John Scott Russell made an experimental study of the Doppler effect (1848).

The Doppler effect for electromagnetic waves such as light is of great use in astronomy and results in either a so-called redshift or blueshift. It has been used to measure the speed at which stars and galaxies are approaching or receding from us; that is, their radial velocities. This may be used to detect if an apparently single star is, in reality, a close binary, to measure the rotational speed of stars and galaxies, or to detect exoplanets. This redshift and blueshift happens on a very small scale. If an object was moving toward earth, there would not be a noticeable difference in visible light, to the unaided eye.

Note that redshift is also used to measure the expansion of space, but that this is not truly a Doppler effect. Rather, redshifting due to the expansion of space is known as cosmological redshift, which can be derived purely from the Robertson-Walker metric under the formalism of General Relativity. Having said this, it also happens that there are detectable Doppler effects on cosmological scales, which, if incorrectly interpreted as cosmological in origin, lead to the observation of redshift-space distortions.

The use of the Doppler effect for light in astronomy depends on our knowledge that the spectra of stars are not homogeneous. They exhibit absorption lines at well defined frequencies that are correlated with the energies required to excite electrons in various elements from one level to another. The Doppler effect is recognizable in the fact that the absorption lines are not always at the frequencies that are obtained from the spectrum of a stationary light source. Since blue light has a higher frequency than red light, the spectral lines of an approaching astronomical light source exhibit a blueshift and those of a receding astronomical light source exhibit a redshift.

Among the nearby stars, the largest radial velocities with respect to the Sun are +308 km/s (BD-15°4041, also known as LHS 52, 81.7 light-years away) and −260 km/s (Woolley 9722, also known as Wolf 1106 and LHS 64, 78.2 light-years away). Positive radial velocity means the star is receding from the Sun, negative that it is approaching.

An echocardiogram can, within certain limits, produce an accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the ultrasound beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, abnormal communications between the left and right side of the heart, leaking of blood through the valves (valvular regurgitation), and calculation of the cardiac output. Contrast-enhanced ultrasound using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.

Although “Doppler” has become synonymous with “velocity measurement” in medical imaging, in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (when the received signal arrives).

Velocity measurements of blood flow are also used in other fields of medical ultrasonography, such as obstetric ultrasonography and neurology. Velocity measurement of blood flow in arteries and veins based on Doppler effect is an effective tool for diagnosis of vascular problems like stenosis.

First, a Story:

You hear about the kids book that explains the Big Bang and Big Crunch to children? “One Shift, Two Shift, Red Shift, Blue Shift.” By Doppler Seuss.

Second, a Song:

The Chromatics are a high-energy vocal band on a mission to delight audiences with a full spectrum of songs about science, technology, life, and their intersections. They have taken their astronomically-correct a cappella songs, a project called AstroCappella, from coast to coast, and their CD has flown in space (for realz!). Back down on earth they have captivated young and old alike at the Kennedy Center’s Millennium Stage, the National Air & Space Museum, the Mid-Atlantic Harmony Sweepstakes, and numerous science fiction conventions, First Nights, festivals, concert series, and private parties. Their CDs have been nominated for multiple awards. Celebrating 25 years together they are a mainstay of the local music scene and still bring a youthful exuberance to their fun-filled, colorful, and scientifically accurate performances (per https://www.thechromatics.com/about.shtml).

Here are The Chromatics performing their a cappella song “Doppler Shifting”.  I hope you enjoy this!

(https://www.youtube.com/watch?v=3DPRq7jUbiU)

Thought for the Day:

“Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the drug store, but that’s just peanuts to space.” – Douglas Adams

Cheers!

Have a great day!

Dave & Colleen

© 2021 David J. Bilinsky and Colleen E. Bilinsky