Sci-fi physics — sound ten times faster

Problem

Imagine sound in air travelled at $3{,}4\;\mathrm{km/s}$ instead of $343\;\mathrm{m/s}$. What effects on music? And on the perception of thunder?

Solution

What changes and what doesn’t. The speed of sound becomes $\approx 10$ times greater. The frequency at which a string or an air column vibrates is not fixed by the speed of sound in air, but by the properties of the instrument; so the notes stay unchanged in pitch.

On music. From the relation $\lambda = v/f$, at fixed frequency the wavelength is multiplied by 10. The resonance modes of rooms and wind instruments depend on $\lambda$: concert halls and organ pipes would need to be ten times bigger to resonate at the same frequencies. Room acoustics would need to be completely rescaled.

On thunder. The flash-to-thunder delay is $t = d/v$: with $v$ ten times greater, the delay collapses by a factor of ten. The “3 seconds per kilometre” rule would become “0.3 seconds per kilometre”: it would become almost impossible to estimate the distance of a storm by eye, counting seconds.

$\ev{\text{Frequencies unchanged; } \lambda \times 10;\ \text{hall acoustics to rethink; flash-to-thunder delay} \div 10.}$

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Topics: Onde Concepts: Periodo e frequenza Skills: Analisi di casi limite e fantafisica