Put your hand on your throat and say thing, elongating the th sound. Now do the same with then. Notice a difference? In the short video below, YouTuber Tom Scott explains how your vocal cords vibrate when you produce certain sounds, such as the th in then or there, but don't when producing others, such as the th in thing or thick.
It's the same contrast with S and Z, or F and V. That is, both S and F lack this buzzy vibration (they're voiceless), while Z and V have it (they're voiced). Unless, incidentally, you're whispering—which is why, when you have laryngitis and your vocal cords are inflamed, you can only whisper.
If you're not too squeamish, you can also watch this fascinating—but decidedly odd-looking—video of the vocal cords moving during various sounds, produced by snaking a flexible camera and small light down someone's throat:
The vocal cords—more properly called vocal folds, since they're really folds of membrane, not cords like on a guitar—produce sound by constricting into a small opening, through which the air passing out from your lungs creates a rapid vibration. It's the same effect that enables sound from the reed of a clarinet or the whistle from a blade of grass.
Although we're not consciously aware of what exactly our vocal cords are doing while we speak, whether or not they're vibrating at any given moment has lots of implications for the English language. For example, it can make the difference between a noun, such as house, and a verb, such as to house. It also accounts for why the S in dogs sounds like /z/, but the S in cats sounds like /s/, which is something that even young children are sensitive to.
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