When I’m filling a big jug of water, why does the pitch of the stream hitting the water inside get higher as it gets closer to the top?
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The sound you are hearing is due to vibrations in the air, inside the jug. The air in the jug is being pushed back and forward at a particular frequency (so many wobbles per second), and that causes the air next to it to be wobbled, and so on all the way to the air in your ear, which causes your ear to wobble, which tells your brain what sound you heard. The frequency relates to the pitch; the higher the frequency, the higher the pitch.
Linked to the frequency of the air wobbles is their wavelength; roughly, this tells you the distance between the two bits of air that are wobbling in sync. Wavelength is kind of the opposite of frequency; the shorter the wavelength, the higher the frequency, the higher the pitch.
To get a clear note you need a particular kind of wave called a standing wave, and that has specific rules on wavelengths allowed. In the case of our water jug there has to be a fixed point on the bottom (where the ‘solid’ water surface is, as the air there can’t be pushed down and wobbled), and there must be a completely free point (for maximum wobbling) at the opening (where the air is free to move around however it likes). And this limits the possible waves we can get in the jug.
There are a neat [set of diagrams here, on the left](https://www.acs.psu.edu/drussell/demos/standingwaves/Opentubeoneend.jpg) ([source](https://www.acs.psu.edu/drussell/demos/standingwaves/standingwaves.html)) – don’t worry about the maths, just that these are tubes open at only one end (like our water jug) and show the possible waves that can form, as the wave needs to be “fixed” at the closed end (where the water is), and “free” at the open end.
The longest wavelength (so deepest note) we can get is the top one; when the wavelength is 4 times the length of the tube/jug (then we get other possible wavelengths at 4/3rds, 4/5ths, 4/7ths the length of the tube and so on). As water fills up our jug, the length available for waves to form (“L” in that diagram) gets shorter. So the maximum possible wavelength gets shorter, and so the deepest sound we hear gets higher in pitch.
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