In crossing the pedestrian bridge over the Salzach river, every step takes me away from the famous view of the fortress over Old Town classics of steeples and baroque in Salzburg. Before I get to where I want to be, I have to cross a busy street in the afternoon rush which has come to a halt. Wailing sirens approach and recede as red and white “Rettungswagen” race to the emergency situation somewhere in the city. The cyclical lights are in my favour, and upon turning the corner, I see the sign that tells me I’ve arrived.
One self-assigned goal during three weeks of travel within Austria was the search for places associated with physicists and mathematicians of my youth. And by youth, I mean the tender twenties when all I cared about was a succinct explanation of the natural world through various equations1. In Alpbach, I found Erwin and Annemarie Schrödinger’s grave. In Vienna, I found Ludwig Boltzmann’s grave. Here in Salzburg across the street from the Mozart family house, I found Christian Doppler after whom the Doppler effect is named.
Where Christian Doppler was born
On the east/right flank of the Salzach river at address Markartplatz 1 is a building which now houses a perfume store (Nägele and Strubell), a beauty salon, and a tapestry shop (Fine Arts Gobelins). Two tablets one each on the outside northeast- and northwest-facing walls highlight the building’s famous occupant. The building is located within the “core zone” for UNESCO’s 1996 inscription of Salzburg’s historic centre as World Heritage Site.
Constructed at the end of the 18th-century, the building at Makartplatz 1 is one of few remaining buildings in the “classical architectural” style. Christian Doppler was born inside this building in 1803 to a family of stonemasons. His education took place in Salzburg and Linz; in Vienna he studied physics and mathematics. He landed professorships in Prague and Schemnitz (now Banská Štiavnica), before returning to Vienna. His poor health continued to worsen, and he moved his family to Venice where he died in 1853.
Even if you didn’t know the name of the scientific principle, you’ve encountered the physics before. In an emergency, a police, ambulance, or fire department vehicle screams down the road, and you notice the change in pitch of the siren. The change from high- to low-pitch when the vehicle goes past is the Doppler effect which describes an observed change in frequency caused by the velocity (speed and direction) of the moving object2. In the case of the siren, the actual frequency of the siren remains unchanged, but the moving vehicle to which the siren is attached either “squashes” the sound waves in front and “stretches” the sound waves behind. With the speed of sound at about 1230 kilometres per hour (765 miles per hour), an emergency vehicle at 120 km/h (75 mph) is travelling at about 10% of the sound speed.
During his time at the Prague Polytechnic (now Czech Technical University), Doppler wrote about the effect of velocity-induced frequency shift for the first time in his 1842 paper “Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels” (On the coloured light of binary stars and other stars in the heavens). A full copy of his paper in German is available here (doppler.net), here (archive.org), and here (wiki). There’s also a summary of his paper in English here (wiki).
The Doppler effect can be calculated with the following equation:
where v : speed of sound, typically 344 metres per second (20°C);
vsrc : speed of the source, in metres per second (m/s);
fobs : observed frequency, in Hertz (Hz); and
fsrc : source frequency, in Hertz (Hz).
For a receding source, vsrc is positive; for an approaching source, vsrc is negative.
Ambulance vehicle A1 emitting a siren at 1000 Hz is receding at a speed of 80 km/h or 22 m/s. At the same time, ambulance vehicle B2 emitting a siren at 1000 Hz is approaching at a speed of 80 km/h or 22 m/s. For a stationary observer, they’ll hear A1’s siren at a (lower) frequency of 939 Hz, and they’ll hear B2’s siren at a (higher) frequency of 1069 Hz.
Applied examples of the Doppler effect include:
- emergency sirens: police, fire department, ambulance
- home: intrusion detectors, automatic door openers
- radar: weather radar, police radar, missile early warning systems
- medicine: Doppler echocardiography, Doppler ultrasonography
- astronomy: signals and images from unmanned space probes in our Solar System, discovering exoplanets, binary stars, high-redshift galaxies
Except the image illustrating the Doppler effect and the YouTube video, I made the photos above on 21 and 22 May 2018. This post appears on Fotoeins Fotografie at fotoeins DOT com as https://wp.me/p1BIdT-bYz.
1 It’s easy to wonder at the simplicity and practicality of Newton’s 2nd Law (F equals m times a), but a generalized version of Newton’s 2nd Law appearing in the form of the Schrödinger equation rocked my world. Fortunately, that was merely the beginning.
2 To make things even more interesting, the inverse Doppler effect has been observed in substances with negative refractive indices.