# Why is the sound of filling a container with liquid always the same regardless of container?

I found a similar question asking why the sound changes as fluid level changes. Foobarbeque's answer mentions Helmholtz Resonance, and that the frequency depends on cavity volume, length of neck and opening area.

My question is: why does the sound sound similar between vastly different vessels?

When I say "the sound", I am not sure of the correct term - is it the tone? pitch? I am assuming "frequency" mentioned above is correct, but I mean the note always seems to go from low to high - but through exactly the same range regardless of vessel size. That is, it is not the case that one vessel starts from a lower low, or another ends on a higher high. If I fill a 25L plastic drum with a hose, or a drinking glass from the kitchen tap or any other type of vessel, the range of notes appears to be identical regardless of vessel shape. Why? And can you describe exactly what is making the sound?

• Maybe it's because the ratio of volume to opening size is always approximately equal between the vastly different vessels I encounter (ie - trying to think how volume, length of neck, and opening area may relate in a constant way)? PS. Would love to know how "neck" is defined, in order to calculate "length of neck" - but that's an aside, or to post to the other question. Dec 22, 2016 at 1:41
• Do you have any evidence for your claim about the lows and highs being the same? Dec 22, 2016 at 9:52
• Nope. My ears.. Dec 23, 2016 at 1:04
• The range which can be heard will be restricted in any case by the audible frequency range - ie the highest and lowest frequencies which the human ear can normally detect. But I doubt your observation is correct. Test tubes do not start with notes as low as large metal drums. foobarbecue's answer (which you have obviously read) seems to contradict your claim. Unless you can corroborate your observation, users might be suggesting explanations for a phenomenon which may not actually exist. IMO, the 1st step in any scientific explanation is to verify the phenomenon. Dec 23, 2016 at 5:40
• I disagree with your assertion that the shape of the vessel makes a difference in the sound. It does make a difference. Now the total range of pitch may be the same but that's due to the range of human hearing, but the overtone mixtures and the rate of pitch change are going to be totally different. Mar 19, 2019 at 3:34

You ask, for water containers across a variety of volumes,

"...the range of notes appears to be identical regardless of vessel shape. Why? And can you describe exactly what is making the sound?"

The short answer is they are definitely not identical. However, the container-dependent effects on the sound are small in comparison to the source-dependent effects.

Here's why.

It turns out that air bubbles are the primary source of sound in pouring water. In the freely available paper by Zheng and James 2004 entitled Harmonic Fluids, the authors state:

Ironically, the complex visible motion of the air-fluid interface causes relatively little sound, in part because visible surface motions are inefficient radiators of sound waves at audible frequencies [Bragg 1920]. Instead, the fluid shape vibrates harmonically at audio frequencies due to the microscopic oscillations induced by internal air bubbles, and acts like a shape-changing 3D loudspeaker.

The model, itself (which you can actually listen to examples of here) relies on a dual-domain Helmholtz Green's function, such that it includes two boundaries:

• the boundary of the liquid and it's container, $\Gamma_s$
• the boundary of the liquid and the air (where our ears are), $\Gamma_a$.

Both obviously depend on the form of the container! However, as I understand it, the size and number of bubbles has much more influence over the source strength and frequency of the pouring event.

One experiment you can do to see if this makes sense in practice is to change the way the stream enters the container (angle, height above fluid surface, diameter of the stream, etc.) Try to change the number or size of the bubbles. See how that changes the sound. Alternatively controlling for those factors with different containers may isolate the effect of the container's form.

• Fantastic answer. Thank you for taking the time to explain this - I had not anticipated that the answer relates to the air bubbles in the fluid. That the fluid-container boundary and fluid-air boundary each contribute to the sound is perhaps what I expected, which is why a consistent sound was not expected. The notion that the fluid-bubble interfaces have a greater contribution makes more sense of my observations - especially as I'm generally noting the effect at kitchen taps - hence not varying the bubbles. Feb 13, 2018 at 23:44
• Regarding Sammy's earlier question about evidence for the claim that the sound is similar/identical despite vessel, since posting this question I have learned about spectrograms and have a basic app to produce them. I will carry out a few kitchen sink experiments with your notes on the bubbles in mind and see whether the spectrograms can visually demonstrate what I am hearing. Feb 13, 2018 at 23:46
• @youcantryreachingme if you appreciate the answer, would you consider accepting it? Feb 14, 2018 at 0:17