Why does the hiss of foam rise in pitch?

Question

When you pour an aerated drink into a glass or some soapy water into a bucket, you get foam. If you listen carefully, you will hear a characteristic hissing sound from the foam (See video).

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I noticed that this sound rises in pitch as the foam fades away. This is a spectrogram of the hissing sound using Audacity. The brighter parts are louder, you have time on the horizontal axis and frequency on the vertical axis.

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The bright part till the 11-second mark is the sound of water falling into the bucket. The dark part from 11 seconds to 17 seconds is the hissing sound from the foam. You can see that the lower frequencies mostly die out after the 13-second mark.

The experiment was repeated and the pattern remained the same. The low frequencies die out after about 2 seconds of hissing. Note that this is roughly the same time taken for the foam to disappear in the video.

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Why does the pitch rise when the foam becomes thinner ? Does this have something to do with the size of the bubbles remaining in the foam? (larger bubbles pop faster, smaller bubbles last longer)

Answer 1

Could be also that as time passes and the foam subsides the ratio of the number of popping small relative bubbles (generating higher pitched noise) to the number of large popping bubbles (generating lower pitched noise) increases with time. Seems to me from your photo provided that at any moment in time the larger bubbles are rare and the vast amount of bubbles are in average relative small in size.

Also another contribution to the increasing pitch noise could be also that larger bubbles last longer before they pop. Anyway this is a complicated many-body problem that could result in a novel paper publication.

From a pure mechanical point of view the elasticity of the fluid falling in the cup behaves like the decaying vibrations of a spring. In the beginning the vibrations are large in displacement thus lower frequency creating foam where the molecules have corresponding low frequency of vibration therefore creating large number of large size popping bubbles as the vibrations die off and the fluid and foam starts to relax and calm vibrations are becoming of less displacement and higher frequency. Therefore size of generated bubbles becomes progressively smaller and popping bubble sound higher in pitch. A good analogy is this coin trick as a model o how the molecules of the foam vibrate:

falling coin on table sound

Listen to the sound of a spinning Euler's disc as vibrations decay:

Euler Disc

Answer 2

The sound resonance frequency depends on the dimensions of the unfilled portion of the glass. For example, if the velocity of sound is, roughly, 300 m/s, the sound wavelength is 5 cm for the frequency of 6 kHz, which is commensurate with the size of the glass.

EDIT (10/19/2021): The OP asked: "If I remember correctly, the rise in pitch started when the foam started to disappear. If the pitch change was due to the air column of the glass, the pitch should've been higher when the foam is thicker, right? " My answer: " I am not sure. I would think foam's density is close to that of air, so it does not reflect sound as well as liquid, so the resonance frequency will still be defined by the dimensions of the unfilled part of the glass (where the space filled with foam is considered "unfilled"). However, the sound resonance frequency is also defined by the sound velocity, and sound velocity is lower in foam than in air (Chinese Phys. Lett. 29 104301, iopscience.iop.org/article/10.1088/0256-307X/29/10/104301), so the resonance frequency is lower when there is foam."

Answer 3

Among other answers (bigger bubble -> lower sound, and less larger bubbles in the first place) I would assume that you hear the sound of bubbles on the top. Bigger bubbles are on the top as they are (if represented as particles) lighter. They pop and the layer of smaller bubbles appear on the surface. Then it repeats until there are no bubbles.

Answer 4

My thought was to start with the Helmholtz resonator, so I search and found this article.

Further searching revealed another interesting article link, which addresses and solves the same problem you are describing, with HPC simulations. They derived a quite complex model for the frequency.

Other article you may already know Noise Generation by Air Bubbles