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<   No. 4366   2020-10-19   >

Comic #4366

1 Serron: A relativistic hyperguitar... How do people invent these things?
2 Salesman: Well, the vibration frequency also depends on the length of the strings.
3 Salesman: The first attempt accelerated the guitar to relativistic speeds along the direction of the strings, to induce Lorentz contraction.
4 Iki Piki: That sounds tricky to handle.
4 Salesman: First band to use one still hasn’t found their bass player.

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After writing the previous strip, concentrating mostly on the tension and the mass of a vibrating string, I considered how a relativistic hyperguitar might vary the pitch of notes by changing the third relevant variable, namely the length of the strings.

Fortunately, special relativity has a way to do that too! All you have to do is give the strings a velocity close to the speed of light, in the same direction as the string is stretched.[1] Then Lorentz contraction will make the strings shorter as viewed from the frame of the audience, thus increasing the pitch of the musical note.

There is a slight complication, as the Doppler effect will also affect the pitch of the note. And the guitar will easily break the sound barrier, causing a sonic boom. And it will also ionise the atmosphere of the planet you're watching the performance on, causing some other minor inconveniences such as an immediate and colossal overdose of x-rays. Although that probably won't kill you, because the nuclear fireball will do it first. See this What If? write-up for a general idea.

[1] Technically this would also work as long as there is some component of velocity close enough to the speed of light in that direction, so the exact direction is not critical.

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