# Is, in terms of sound, pouring water in a bottle the analogous of blowing into it?

When we pour some liquid in a closed container, for instance a jar or a bottle, we usually hear two (acoustical) noises: one is the classical turbulent (I guess white) noise, that in my view is closely related to the turbulence of the fluid flow as it starts hitting the bottom of the container. The other, is a very characteristic and coherent sound, that any of us learned to recognise as a child, and has an higher frequency as the fluid fills completely the container.

Now, the fact that the frequency increases should be explainable with the fact the fluid behaves as a wall for the remaining empty part of the bottle, thus creating a shorter and shorter closed pipe. At the nozzle, the water entering might have a behaviour resembling that of a blow or a whistle, and then I kind of imagine the the phenomenon as being the analogous of a person whistling in a pipe of a certain shape.

Am I right? Can anyone develop a little bit more the underlying reason for this behaviour? And also, is there any literature on this sound, on its dependence on the shape of the bottle and on the liquid used (the surface tension may influence the wall-behaviour of the free interface)?

• Commented Apr 10, 2015 at 20:10
• Note that this also happens with open pipes i.e. drinking glasses. Commented Apr 22, 2017 at 18:39
• are there any existing physical modeling approaches that approximate this? sounds like you can get much of the way there by using Hemholtz resonance of the vessel (possibly approximated as a sphere to start) plus white noise to simulate the water flow but I wonder if anything more detailed already exists Commented Aug 2, 2020 at 21:55
• in particular I wonder if Joukowsky's equation is relevant here in terms of free-flowing water hitting the surface Commented Aug 2, 2020 at 21:58

## 2 Answers

The sound you hear is somewhat, but not completely, analogous to someone blowing over the top of the bottle.

The air-filled part of the bottle is a resonant cavity, as described in the answer to this question as mentioned in a comment above. And it's being excited by the noise of the water filling it, which is some general random (but I suspect not terribly white) noise from the turbulence, as you say. The cavity is then acting as a filter, producing a spectrum which has a big peak around the resonant frequency of the cavity, and this is the pitched note you are hearing: it rises as the cavity gets smaller.

To this extent it is the same as blowing over the top of a bottle: you're hearing the resonance of the cavity. What isn't the same is that, when you blow over the top of a bottle there's a dynamic instability in the airflow over the aperture which puts more energy into the system, so you get a much stronger note. That's missing in the case of the bottle just being filled.

Although it is kind of cheating, an interesting way to explore this sort of thing is to play with white noise driving an electronic audio-frequency filter. These often have adjustable characteristics, including variable Q, and you can get everything from slightly peaky white noise to a more-or-less pure tone as the filter self-oscillates (of course, a bottle won't do without air being blown over it, as nothing is supplying it with energy).

Excitation is due to interaction (exchange of momentum, changes of volume and force) of the droplets with the liquid surface. The air volume in the bottle has its own characteristic response which emphasizes particular frequencies of the excitation. During filling, the air volume decreases and small things tend to vibrate more at higher frequencies. A small volume makes higher frequencies audible than a larger volume.