The Beauty of Math - Sonic Booms

Have you ever wondered what a Sonic Boom really was? Consider this great explanation. Using this reasoning, what do you think a sonic boom looks like in water? Could we ever have a "photo boom," a sonic boom with light instead of sound?

For those with more advanced knowledge, how could you mathematically describe a sonic boom with a coordinate plane? What MACH creates the loudest sonic boom? What happens if the speed of the plane is variable? Feel free to respond with answers, hints, or ideas of where to go with these questions.

Image credit: NASA

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Easy Math Editor

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Comments

I would predict that around Mach 1 would create the loudest sonic boom. The sound produced from every moment in the plane's flight stays with it; therefore, as it passes over you, all of the sound produced at any time would hit you at the same time.

Daniel Liu - 7 years, 6 months ago

That's what I was thinking; although I'm sure we could prove it mathematically.

Bob Krueger - 7 years, 6 months ago

In addition, I am assuming that you are at the same height as the plane. If you were, for example, 1 kilometer under the plane, the speed for maximum loudness would noticeably change.

EDIT: I realized that not only would the speed for maximum loudness change, the range in which it has the same maximum loudness would also change. There would be a range of different speeds that would produce maximum loudness if you were 1 km under the plane. Correct me if I am wrong on this point.

Daniel Liu - 7 years, 5 months ago

A sonic boom with light is the Cerenkov effect, which is used all the time in particle detectors to see high energy particles hitting the detector. The "vacuum Cerenkov effect" which is the emission of light spontaneously in vacuum is one of the primary ways we use to accurately test special relativity.

David Mattingly Staff - 7 years, 5 months ago

Fascinating!

Bob Krueger - 7 years, 5 months ago

In my opinion, it wouldn't be a photo boom, it would be a photo flash. Also, I agree with Daniel Liu about the Mach 1 creating the largest sound.

Sharky Kesa - 7 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$