Friday is here again, and with it the weekly "A Taste of Physics" column — number 25.
This week: the Prandtl–Glauert singularity, Bernoulli's equation, and the speed of sound.
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The aircraft in the video is flying close to the speed of sound — Mach 1.
Flying at such a speed produces two effects that are unrelated to each other:
The first is the formation of a cloud of water droplets behind it.
The second is sonic booms powerful enough to shatter windows, as aircraft of the Israeli Air Force repeatedly demonstrated over Lebanon.
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How does it work?
The sonic booms are created because the aircraft "compresses" the air it strikes, generating shock waves within it.
These waves cause sound waves to concentrate in narrow bands rather than spreading evenly through the air, which is why they reach our ears as a sonic boom.
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The vapor cloud behind the aircraft is a separate phenomenon, known as the "Prandtl–Glauert singularity."
As the aircraft approaches the speed of sound, the airflow around it becomes irregular — in certain regions it exceeds the speed of sound, while in others it is slower.
As a result, the air density around the aircraft's tail drops, causing it to cool.
When air cools it can hold less water vapor, so the vapor condenses into tiny droplets that appear to us as a cloud.
The reason low pressure causes air to cool is described by Bernoulli's equation.
The equation describes the balance of forces acting on a fluid or gas as a consequence of the law of conservation of energy. It shows that as the velocity of air increases, its pressure decreases, causing it to expand and cool.
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And finally — what is a singularity?
A singularity denotes a point at which the behavior of a system becomes undefined or infinite — meaning there is no way to describe the state at that point precisely in mathematical terms.
In the physical world, of course, states are always finite and well-defined at every moment in time; however, the values of those states cannot be predicted in advance with exact precision.
Shabbat Shalom 🌹
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