Well done for doing the low range calculation.

Adding to @Schmuddi's point on the importance of higher frequencies: In telephones, audio was/is usually low-pass filtered with a cutoff around 2700-3000 Hz. This works well enough for most purposes, but is the reason why it can be difficult to distinguish for example a bare "S" from a similarly bare "F" in a telephony conversation (where the higher harmonics are important). Many two-way communication radios are likewise lowpass filtered with a very similar cutoff frequency, this time in order to conserve radio spectrum. The traditional workaround is to say "Sierra" or "Foxtrot".

@Schmuddi you may be right. It's a tough call on how clearly they would sound. Those higher frequencies are the harmonics of the fundamental, starting at 1/10 of the normal frequency makes is hard to reach those ranges, though the louder voice could reach those harmonics. Parts of our body also act as resonating chambers, a larger body will have a lower frequency. I omitted this in my answer but vibrations are heavily mass dependent, thanks to the square cube law not only will the anatomy be larger but the parts will be heavier. Further dropping the produced frequencies.

Though the vocal cords would be longer, they'd also be much thicker. Would there be any sound at all with this? Would the air flow be great enough, and density of the air be great enough, to vibrate such cords?

@Paul I think it would be safe to assume that the lungs/diaphragm would be strong enough to get them to vibrate. What that frequency would be is very hard to tell. My guess is very low.

Great, now for comedic effect I am imagining a giant in which everything was scaled up except the vocal cords, which actually got smaller, resulting in a squeaky, high-pitched giant.

Except the waveshape at the base frquency is not a sine wave. It is basically just a pulsing square wave. It has many higher harmonics it would definitely be audible to us. The vowel formants would be much more important and you haven't even discussed those.

The physics of resonance for a complex shape are very different from the physics for a simple string. I think your simple calculation is just straight up wrong.

@Octopus Where are you getting that the frequency is a square wave? Also, I did mention the harmonics. It's just going to be difficult to reach them due to how many it will take to get to our common vocal range. We may be able to hear them, but they will be hard to understand.

@BobTheAverage That's why I said rough approximation. I've probably actually overestimated it by a decent margin. With larger cavities to resonate in and heavier body parts (thanks to the square-cube law), their voice is bound to be very low.

The base frequency certainly isn't the dominant frequency. The most basic sound that comes from the vocal cords is a slightly rounded version of a pulse wave, but many things flavor it so a voice can sound "breathy" or "bright", for example., this is before it even reaches the throat and mouth which act as resonating chambers. The explanation here is rather elementary and naive at best.

@Octopus I've already mentioned that my answer was an approximation. Barring a full simulated model or actually speaking to a giant I'm not sure of a better way to approximate it. Your plots show exactly what I was trying to convey: starting at a lower base frequency means that it will take more harmonics to get into the vocal ranges. The plots have a base frequency of 100 hz and lose 9 to 12 dB or intensity per doubling. Starting at 13Hz, 26, 52, 102 you are already looking at 27 to 36 dB of loss by the time you get to their starting points.

I think this is a non argument, whatever eventuates the voice is going to be MUCH lower, and the calculations are not going to be precise because there are just too many factors. So while Johns calculation is very simple, it does make a good point

I wouldn't say it would have to be much lower, elephants for example (livescience.com/22071-elephant-calls-vocal-cords.html) use vocal chords 8 times the size of ours, but since they can tense up tighter due to being larger and stronger muscles they can make high pitch sounds, as well as ones far lower pitch than we can. As a guess, I would estimate that the squeak at the end of their trumpet sound is about as high pitch as a girls voice.

@PaulS: the elephant's trumpet sound is produced by a different apparatus altogether from the vocal chords. (More like a whistle, in that respect). But their vocal chords can produce tones too low for the human ear to hear

You can tighten the thickest string on a guitar to get pretty high notes, but it will break long before it reaches what can be done on the thinnest

Although you say “generally speaking”, I don't think it is correct to say that larger things vibrate more slowly. Resonances change somewhat, diffusion and propagation allow for longer durations of time. Larger things can produce and resonate at lower frequencies, so far as I know, but everything usually vibrates with whatever wave passes through it.

@can-ned_food All things being equal, the resonant frequently of a large object is lower than that of a smaller object. A different frequency will of course propagate though whatever it pleases, but the object will ring at its resonate frequency.

@JoeKissling I think that's rather much what I said; I was also saying that you should either use a different word from “vibrate” or further qualify your statement. I.e., only things which vibrate in such a way that resembles a plucked string will operate like one. There is a reason why a longer string, when plucked, will vibrate at a lower frequency than a shorter string.

Possibly worth mentioning in the accepted answer: Giant speech would also be much slower, for at least two reasons: 1) Low-pitched vowels require more time to sound different from each other. 2) More significant, the tongue and lips would probably take proportionally longer to flit from syllable to syllable, as the mechanics of speech are pretty much at the limit of our muscular rapidity and agility. 3 words/second is fast for humans and giants might struggle to articulate even one word every 3 seconds.

Repeating a point in the comments, but since their eardrums are also much larger, presumably they'd be able to hear much lower frequencies as well.