Next Monday show: speakers. Upload this episode backwards.
Also there is a maximum loudest possible sound. It depends on ambient air pressure.
Whatās a sound wave? Pressure oscillations up and down. Pressure can increase basically infinitely, but you canāt go below 0. So the air itself clips. At sea level itās around 194 dB.
Rocket launches can achieve this.
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I guess thatās true because of the nature of a human ear and air. But letās say you had an ear that could āhearā any wave. What is the limit on an electromagnetic wave traveling in a vacuum? Obviuosly it canāt go faster than the speed of light, but the wavelength and amplitude can be anywhere from 0 to infinity, right?
Not infinity, though unsure what that upper limit would be. Once the photons in the electromagnetic wave hit 299,792 kilometers per second, thatās where it would peak.
The wavelength of a photon canāt be zero - it would have infinite energy then. The energy of a photon is given by E = hc/Ī», where h is Planckās constant and Ī» is the wavelength of the photon.
The smallest meaningful distance is the Planck length: 1.616e-35 meters. A photon with that wavelength would have energy
E = 6.626e-34 * c / 1.616e-35 = 12 GJ
For reference, the energy from combusting a barrel of oil is about 6 GJ.
However, we have to make sure itās not so small we create a black hole. Per good olā E=mc^2, the mass of 12 GJ is 1.367e-7 kg.
Schwarzschild (black hole) radius is given by
r = 2Gm / c^2 = 2.03e-34 meters
2e-34 meters is about 12 Planck lengths. So our photon collapsed into a black hole far before we squeezed down to 1.
The smallest we could possibly go would be where the Schwarzschild radius exactly matches the wavelength. Set those equal to each other:
2Gm / c^2 = Ī»
Via E=mc^2, we can substitute mc^2 for energy in the photon energy formula. Solving for m gives:
2Gm / c^2 = hc / (mc^2)
m = sqrt(hc / (2G)) = 3.857e-8 kg
3.857e-8 kg is 3.466 GJ - the limit for energy a photon could have before it collapses into a black hole. It works out to a wavelength of 5.7e-35 meters, or about 3.5 Planck lengths.
You couldnāt make an āearā to āhearā any of these waves though - that amount of energy in a single photon would destroy whatever matter it ran into. And then the resulting high-energy particles from that collision would also destroy whatever they ran into. And many more times down the chain as well for good measure.
Practically speaking, itās difficult to create super-high energy photons. You can google āultraviolet catastropheā if you want to read about when physicists were figuring out why we donāt see that kind of thing very much. Amplitude could be arbitrarily high though.
@Clinton photons in a vacuum can only go the speed of light. Thereās no ramping up to c or anything - theyāre already there from the instant of emission to absorption.
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