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Let me make one thing clear: I am fully aware that the change in timbre comes from the change in acoustic wave speed when going through a different medium (just like light).

However, would I not need to have helium in my ears to hear the change in timbre? The medium in my ears is air, so the timbre should go back to normal once it leaves the helium boundary, right? Say if light goes from glass to air it will speed up, but it will slow right back down as soon as it goes back into glass again, so if I was in the glass, I would never experience the speed of it in air. Why do acoustic waves seem to not have this behavior?

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To a very rough approximation we can say that frequencies of speech are selected by standing waves in the speakers mouth, larynx etc. If they breath helium the speed of these standing waves increases but their wave length, being constrained by dimensions of their body, remains the same. This results in higher frequency sounds produced. (think $f=v/\lambda$)

The speed of sound waves changes as sound goes from one medium to another but the frequency does not. (Each wave in helium produces one wave in air.) So, the timber of the sound is determined when it resonates in the speaker, changing the speed of the waves later doesn't change their timbre.

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Keep in mind that frequency is both the wave property that is preserved in a change of medium (both wavelength and velocity change) and the physical property of sound waves that we experience as pitch. So the frequencies you hear in both cases are ones produced by the vocal cords.

Nor do we expect the gas environment of the vocal cords to have a large effect on their vibrational behavior because they are effectively taut stings and their frequencies of vibration are set by their mass density, tension and length.

That said, the vocal system achieves amplification by means of resonant standing waves in the larnyx and throat. This is where the gas dependence comes in. Standing waves are selected by wavelength and that is related to frequency by the wave speed. because Helium (for instance) has a higher speed of sound than air, it is higher frequency modes of the vocal cords that resonate in cavities of the vocal tract (whose dimensions remain approximately constant).

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  • $\begingroup$ okay so $\lambda$ and $v$ change by the same factor in order to keep the frequency the same? I would think this HAS to happen since $f = v/\lambda$ the only way to change both variables an keep the same $f$ is to multiply them by the same factor, effectively multiplying $f$ by 1. $\endgroup$
    – M Barbosa
    Jun 10 '16 at 19:21
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    $\begingroup$ In general when you have a relationship like $c = a/b$ and say "$a$ just changed" you could have $b$ fixed and $c$ changing, $c$ fixed and $b$ changing or both $b$ and $c$ changing. The key observation for wave phenomena is that continuity at the boundary requires the frequency be the same in both mediums, so wavelength must change linearly with speed. But you don't know that just from the math: you have to bring physics into play. $\endgroup$ Jun 10 '16 at 20:43

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