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REVIEW 2 major objections 5 minor 102 references

The Sound of Water: Inferring Physical Properties from Pouring Liquids

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read From the sound of pouring alone, the paper recovers the air-column length, container height and radius, flow rate, and time to fill, by tracking the fundamental axial resonance whose wavelength is linear in the air-column length.

desk verdict A genuinely novel physics-grounded pipeline for pouring analysis, with a real but fixable circularity issue in the headline dynamic metric. read the letter →

arxiv 2411.11222 v2 pith:BVF3ET5M submitted 2024-11-18 cs.CV cs.MMcs.SDeess.AS

Piyush Bagad , Makarand Tapaswi , Cees G. M. Snoek , Andrew Zisserman This is my paper · ORCID
classification cs.CVcs.MMcs.SDeess.AS
keywords pouringsoundspitchdetectionaxialresonancephysicalpropertyinferenceaudio-visualco-supervisioncontainershaperecognitionliquidmassestimationfundamentalfrequency
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper attempts to show that the sound of liquid pouring into a container carries enough information to recover the geometry of the container and the dynamics of the pour, without any visual input. Its route is a physical identity: the fundamental frequency of the air column above the rising liquid obeys $\lambda(t)=4(l(t)+\beta R)$ with $\beta=0.62$, so the wavelength curve is a direct metric for the air-column length. From that curve, boundary conditions give container height and radius, and derivatives give flow rate and time to fill. The authors train a pitch detector without manual supervision, first on simulated pouring sounds and then on real recordings with a physics-inspired visual co-supervision, and report that the resulting model infers air-column length to 0.60 cm mean absolute error, height to 2.27 cm, radius to 1.39 cm, and flow rate to 22.5 ml/s on seen containers. A sympathetic reader would care because it turns an everyday, unlabeled sound into calibrated physical measurements and demonstrates generalization to unseen shapes, materials, and in-the-wild videos.

What carries the argument

The load-bearing object is the axial-resonance wavelength identity $\lambda(t)=4(l(t)+\beta R)$, with $\beta=0.62$ fixed; it converts pitch into a linear metric for the air column. Around this sit four derived formulas: $l(t)=(\lambda(t)-\lambda(T))/4$, $H=(\lambda(0)-\lambda(T))/4$, $R=\lambda(T)/(4\beta)$, $Q(t)=-(\pi R^2/4)\,d\lambda/dt$, plus the early-pour approximation $\tau(t)\approx-\lambda(t)/(d\lambda/dt)$ for time to fill. The detector is an audio transformer trained in two stages: synthetic pre-training on simulated pours, then visual co-supervision on real pours, where a scale factor $\alpha$ links metric wavelengths to pixel air-column lengths and radii. The wavelength curve carries the entire argument, because every physical property is a boundary value, an intercept, or a slope of that curve.

What would settle it

Pour into a transparent cylinder with a ruler beside it at a known constant rate, record audio and video, extract the fundamental frequency from the spectrogram, and compare $l(t)$ from Eq. (5) against the visually tracked water level; if the discrepancy grows with $R$ or with flow rate, or if the apparent pitch is not single-valued, the fixed-$\beta$ linear relation fails.

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Extended reading notes

Core claim

The central claim is that the pitch of pouring water is the fundamental axial resonance of a pipe closed at one end, with a fixed end correction: $\lambda(t)=4(l(t)+0.62R)$, where $\lambda$ is the wavelength of the fundamental, $l(t)$ the air-column length, and $R$ the container radius. If this identity holds over the pour, then the wavelength curve is enough to read off $l(t)$ at every instant, $H$ and $R$ from the boundary at start and end, $Q(t)$ from its slope, and the time to fill from its early behavior. The paper supports the claim by building a transformer-based pitch detector that outputs a wavelength distribution per time step, pre-training it on synthetic pours generated with a differentiable synthesizer, and then fine-tuning it on real videos using the video stream as a weak teacher through the scale-aware equation $\alpha\lambda(t)/4 = l_{\text{px}}(t)+\beta R_{\text{px}}$. Tested on a new dataset of 805 real pouring videos, the co-supervised model outperforms classical and learned pitch estimators and estimates physical properties with the errors reported above, while its features also support container-shape classification and liquid-mass regression on a previous dataset.

Load-bearing premise

The load-bearing premise is that real pouring audio contains one clean, dominant axial-resonance pitch that follows $\lambda(t)=4(l(t)+0.62R)$ at every instant, so every later measurement is a boundary value or slope of that curve; the paper itself shows hemispherical containers and some bottleneck containers violate this.

Editorial extensions

If this is right

  • A single smartphone recording of a pour into a cylinder-like container yields absolute metric estimates of the container and the pour with no manual measurement, with reported mean absolute errors of 0.60 cm in air-column length, 2.27 cm in height, 1.39 cm in radius, and 22.5 ml/s in flow rate on Test set I.
  • Visual co-supervision improves estimates most near the end of the pour, where the audio signal is weak, and that is exactly where radius and flow-rate errors are dominated by $\lambda(T)$ and the slope of $\lambda$, so co-supervision translates into better static and dynamic properties.
  • Pitch-detection features encode shape: an unseen three-way shape classification reaches 90.91% sample accuracy and 92.47% mean class accuracy, and linear probing on a prior pouring dataset gives 1.20 oz mean absolute error for liquid mass.
  • The detector generalizes beyond cylinders to semi-conical, bottleneck, cup, teapot, and wine-glass containers, across glass, plastic, steel, ceramic, and cardboard, and to in-the-wild YouTube pours, although hemispherical containers and multi-modal bottleneck resonances are acknowledged failure cases.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that the same pitch-to-wavelength pipeline could serve as a contact-free calibration device: if the container is known, the formula gives flow rate and total poured volume, and if the flow rate is known, the same audio gives the container's dimensions; a direct test would compare audio-inferred volume against a scale.
  • A natural extension is multi-pitch tracking, since the failure on bottleneck containers with two simultaneous frequency modes suggests treating axial and radial resonances as separate tracks, or using a harmonic-aware architecture, rather than a single fundamental wavelength.
  • Because the relation is stated with a constant $\beta=0.62$, the approach makes a testable prediction about how inferred size errors should scale with container radius; measuring that scaling would indicate whether the fixed end correction is an adequate approximation across the dataset's size range.
  • The result suggests that the metric-ruler claim may extend to other container-filling sounds, such as grains or viscous liquids, as long as an air column with a single dominant resonance exists; this is an extrapolation the paper does not make.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This paper claims that, from only audio of liquid pouring, physical properties of the container-liquid system can be recovered: air-column length l(t), container height H, radius R, volume flow rate Q(t), and time-to-fill τ. The authors derive these properties from the axial-resonance relation λ(t)=4(l(t)+βR) in Section 3, train a wav2vec2-based wavelength-prediction network using simulated pouring sounds and visual co-supervision from a DINO-based video teacher in Section 4, introduce a new 805-video dataset in Section 5, and report quantitative results for these properties, plus shape classification and liquid-mass estimation on an external dataset in Section 6. The central theoretical derivation is mathematically straightforward, and the main empirical concern is the provenance of the air-column ground truth used for the headline result.

Significance. If the empirical claims are taken at face value, the paper makes a meaningful advance: it gives a simple and largely parameter-free physical mapping from pitch to metric properties, demonstrates that a learned pitch detector can outperform classical pitch trackers by a large margin, and introduces a valuable dataset for audio-visual physical inference. The independent manual-ruler evaluation of H and R in Table 3 and the external-dataset mass-estimation results are concrete strengths, and the failure cases in Section 6.4 are honestly disclosed. However, the strongest dynamic-property claim (0.60 cm air-column MAE) currently lacks a demonstrated independent ground-truth source, which is essential before the 'audio as metric ruler' and 'human-like capabilities' claims can be accepted.

major comments (2)
  1. [Section 6.1, Table 2; Appendix A.3; Eq. (10)] The manuscript does not state the source of the air-column ground truth used in Table 2. The co-supervised audio model is fine-tuned with the MSE objective in Eq. (10), where the target is the video network's prediction l_px(t)+βR_px, and the video network is trained on pseudo-labels obtained from temporal-difference heatmaps with a RANSAC polynomial fit (Appendix A.3). If Table 2 evaluates against the same pseudo-label pipeline, the reported 0.60 cm error is not a measurement against physical liquid level but an agreement score with the video teacher, and the apparent gain of co-supervision over the audio-only variant (0.60 vs 0.78 cm) could be largely an artifact of fitting that teacher. This is load-bearing because the 'audio is effectively a metric ruler' claim (Section 3.1) and the claimed 'human-like capabilities' (Section 1) rest on this number. The manual ruler measurements for H and R in Table 3 provide independent support for the static-property chain, but they do not validate the dynamic l(t) curve. Please specify the ground-truth source and, if it is the pseudo-label pipeline, add independent manual or sensor-based liquid-level annotations for at least a subset of videos, reporting both pseudo-label-based and independent errors.
  2. [Section 4.3, Eq. (10)-(11); Appendix A.3] The per-video scale factor α is estimated from the ratio between the audio network's own wavelength predictions and the video network's pixel measurements, weighted by RMS energy, and is then fixed while the same audio network is fine-tuned toward Eq. (10). This makes the co-supervision loop partially self-referential: systematic errors in the pre-fine-tune audio model can be absorbed into α and are then not penalized by the objective. The verification in Appendix A.3 (α in [30,80], inverse relation with container size) is only a sanity check. Please provide a sensitivity analysis, e.g., compute α from ground-truth wavelengths on a subset of videos or from an independent metric-to-pixel calibration, and show how the final property errors in Table 3 change. This matters because α is the bridge that converts audio wavelengths into metric quantities used during training.
minor comments (5)
  1. [Section 5, Table 1] The split arithmetic is unclear: Table 1 reports 18 train containers/195 videos, 13 Test I containers/54 videos, 19 Test II containers/327 videos, and 25 Test III containers/434 videos, while the text says the totals are 18 + 25 = 43 containers and 195 + 54 + 434 = 683 videos, omitting Test II and the overlap between Test II and Test III; please clarify the unique-container counts and how the 122 remaining videos are defined.
  2. [Section 6.4, Figure 15] The caption lists '(a) Hemispherical container (cup)' and '(b) Bottle-neck container', but the body text describes (a) as a bottleneck case and (b) as a hemispherical case; the caption and text should be made consistent.
  3. [Table 3] The column header 'Synthetic ↓' is confusing because the text refers to this model as 'audio-only'; using one consistent name would improve readability.
  4. [Section 6.1, Table 3] The rows for time-to-fill use the notation 'τ 1 4 (t)', 'τ 1 2 (t)', and 'τ 3 4 (t)'; please define this notation explicitly, since it is not obvious that these denote the fraction of the original audio given to the model.
  5. [Appendix A.3] The verification that empirical scale factors are in [30,80] relies on 'generic values' of f, s, and Z, but those values are not stated; please provide the assumed values and units so the range can be reproduced.

Circularity Check

1 steps flagged · score 4.0 of 10

Partial circularity: the headline air-column MAE likely targets the same video pseudo-labels used to co-supervise the audio model; other property estimates rest on independent measurements.

  1. fitted input called prediction [Sec. 4.3 / Eq. (10); Sec. 6.1 / Table 2; App. A.3]
    "To compute length of air column from wavelengths, we rely on Eq. (5). We compare our models with the baselines in estimating l(t) and report the mean absolute error averaged over all time points. ... The (psuedo) labels to train this network are obtained using temporal difference between adjacent frames and classical image processing techniques (Derivative of Gaussian on temporal difference heatmaps) to obtain clean ground truths. ..."

    Eq. (10) is the fine-tuning loss: α·λ_audio/4 = l_px+βR_px, with l_px,R_px from the video teacher. The video teacher is trained on A.3's pseudo-labels (temporal-difference heatmaps + RANSAC). Table 2 reports MAE of l(t) but never states an independent source; the only l(t) 'ground truths' the paper describes are those pseudo-labels. Hence the headline 0.60 cm error can measure agreement with the same curve the audio net was fine-tuned to match, sharing smoothing/lag biases, rather than physical truth; the gain over the audio-only 0.78 cm is partly teacher-fitting. H/R, flow-rate and time-to-fill evaluations use manual rulers and actual fill time, so the circularity is partial.

full rationale

The physics chain from Eq. (3) to Eqs. (5)-(8) is a self-contained derivation from standard organ-pipe acoustics with an externally cited end-correction β=0.62; it does not borrow its conclusion from the learned model. Pitch detection is pre-trained on synthetic pouring sounds generated by the same physics equation, but the model is then tested on real recordings, and the static properties are compared against manual ruler measurements, flow rate against volume/time, and time-to-fill against actual fill duration. The only material circularity concern is the dynamic air-column metric: the audio network is fine-tuned with Eq. (10) to match a video teacher trained on the pseudo-label pipeline of Appendix A.3, and the paper does not state that Table 2's l(t) ground truth is independent of that pipeline. If it is the same pipeline, the 0.60 cm figure is a teacher-consistency score rather than an independent physical measurement. This warrants a moderate score, but it does not invalidate the static-property or cross-dataset results, which are externally grounded; there is no load-bearing self-citation or appeal to a uniqueness theorem by the authors.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No novel physical entities are introduced. The central claim rests on standard acoustics assumptions (axial resonance, fixed end-correction, constant flow rate) and on a per-video fitted scale factor alpha used only during training. The free parameters are alpha (fitted per video) and beta (chosen from literature). The axioms are domain assumptions about the physics of pouring and the camera model, which are stated explicitly but not independently verified within the paper.

free parameters (2)
  • scale factor alpha = per video, estimated in [30, 80]
    Computed as a weighted ratio of audio wavelength to video pixel length (Eq. 10). Encodes depth and camera intrinsics, fitted separately for each training video, used only during co-supervision.
  • end-correction factor beta = 0.62 (fixed)
    Chosen from acoustics literature rather than fitted, but it directly scales the recovered radius R via Eq. (6) and is an input that the central claim depends on.
assumptions (5)
  • domain assumption Axial resonance in a cylindrical container is described by f(t) = c/(4(l(t) + beta*R)) with beta = 0.62.
    Assumed to be the dominant source of the observed pitch; used in synthetic data generation, co-supervision, and property inversion. Section 3.1, Eq. (2).
  • domain assumption The observed fundamental pitch of real pouring audio corresponds to this axial resonance mode.
    Real recordings contain gurgling, radial resonance, and noise; the model is trained to track the axial mode. This is load-bearing because the inversion breaks when the pitch is not clean (see failure cases, Section 6.4).
  • domain assumption Volume flow rate is approximately constant within a single pouring video.
    Needed for the linear l(t) in synthetic data generation and for the time-to-fill derivation. Section 5 and Eq. (8).
  • domain assumption The end-correction term beta*R is negligible compared to H at the start of pouring.
    Used for time-to-fill estimation from partial audio. Section 3.3(iv), Eq. (8).
  • domain assumption The scale factor alpha is constant per video and equals (1/Z)(f/s) for a perspective camera.
    Assumed a static camera with fixed intrinsics and depth; used in co-supervision. Eq. (11).

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Pith. "Pith review of The Sound of Water: Inferring Physical Properties from Pouring Liquids." pith.science (2026). https://pith.science/paper/BVF3ET5M

@misc{pith2026241111222,
  author       = {Pith},
  title        = {Pith review of: The Sound of Water: Inferring Physical Properties from Pouring Liquids},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BVF3ET5M}},
  note         = {Machine review of arXiv:2411.11222}
}
read the original abstract

We study the connection between audio-visual observations and the underlying physics of a mundane yet intriguing everyday activity: pouring liquids. Given only the sound of liquid pouring into a container, our objective is to automatically infer physical properties such as the liquid level, the shape and size of the container, the pouring rate and the time to fill. To this end, we: (i) show in theory that these properties can be determined from the fundamental frequency (pitch); (ii) train a pitch detection model with supervision from simulated data and visual data with a physics-inspired objective; (iii) introduce a new large dataset of real pouring videos for a systematic study; (iv) show that the trained model can indeed infer these physical properties for real data; and finally, (v) we demonstrate strong generalization to various container shapes, other datasets, and in-the-wild YouTube videos. Our work presents a keen understanding of a narrow yet rich problem at the intersection of acoustics, physics, and learning. It opens up applications to enhance multisensory perception in robotic pouring.

Figures

Figures reproduced from arXiv: 2411.11222 by the authors.

Figure 1
Figure 1. Overview of the problem and approach. We train a pitch detector without any manual supervision and rely on physics to estimate physical properties merely from the sound of water. Abstract We study the connection between audio-visual observations and the underlying physics of a mundane yet intriguing everyday activity: pouring liquids. Given only the sound of liquid pouring into a container, our objective is to autom… view at source ↗
Figure 2
Figure 2. Demonstration of resonance in liquid pouring. As liquid is poured in the container shown in (a) of height H and radius R, a sound made up of an increasing pitch (fundamental frequency) and some (odd) harmonics is observed on the spectrogram shown in (b). Two kinds of resonance are observed: axial (fundamental shown as blue circles in (d), first harmonic as green crosses) and radial (fundamental shown as yellow squar… view at source ↗
Figure 3
Figure 3. Model architecture and training. (a) The audio network is based on a wav2vec2 repurposed for pitch detection. (b) The video network is based on DINO repurposed to operate on image sequences to detect length of air column and container radius (up to a scale factor). (c) The audio network is pre-trained on synthetic samples and then fine-tuned on real samples using physics-inspired co-supervision from the video. train… view at source ↗
Figures from the paper (17 more)
Figure 4
Figure 4. Figure 4: Samples of simulated pouring sounds. Our simulator takes in (i) a real sample from the train set as condition, (ii) a random pitch profile and generates synthetic waveform that resembles sound of pouring liquid in a cylindrical container. More samples are shown in Appe…
Figure 5
Figure 5. Figure 5: Examples of containers used in the Sound of Water 50 dataset. The dataset contains videos of pouring liquids in containers with diverse shapes, materials, opacity and background environments. The train set has videos of pouring in transparent cylinder-like containers. …
Figure 6
Figure 6. Figure 6: Sample video sequences from the Sound of Water 50 dataset. (Left) Sample pouring sequences in each of the three container shapes: cylindrical, semiconical and bottleneck. (Right) The corresponding spectrograms of the pouring sounds. Split Opacity Shapes # containers # …
Figure 7
Figure 7. Figure 7: Sound of Water 50 dataset statistics. We show some basic numbers from the dataset. (Left) shows distribution of video duration, (center) shows distribution over container shapes and (right) shows distribution over container material. results are reported in [PITH_FULL…
Figure 8
Figure 8. Figure 8: Where does co-supervision help the most? We find that co-supervision is most beneficial towards the end of the audio where the signal is generally low. This is shown qualitatively on a sample in (a) and quantitatively on Test set I in (b). This helps in more precise ra…
Figure 9
Figure 9. Figure 9: Results on shape recognition from audio embeddings. (a) Latent embeddings learned by the co-supervised audio model encode container shape. (b) On an unseen test set, it is able to recognize the container shapes with a sample accuracy of 90.91% and mean class accuracy o…
Figure 10
Figure 10. Figure 10: Generalization across container shapes. Although our pitch predictor is trained only on cylinder-like containers, it works reasonably well on various free-form shapes encountered in daily use (unseen during training). The theoretical estimate (green curve) is obtained…
Figure 11
Figure 11. Figure 11: Generalization across container materials. Our pitch detector works well for diverse kinds of container materials while the shape (semi-conical) is fixed. The theoretical estimate (green curve) is obtained by assuming it as a cylinder and thus is not perfect and only …
Figure 12
Figure 12. Figure 12: Generalization to in-the-wild videos. We qualitatively evaluate on videos sourced from YouTube. Our pitch detector works very well even on these samples. Notice the variability in the visual inputs and contrast that to the consistency in the audio recordings. Generali…
Figure 13
Figure 13. Figure 13: Robustness to various factors. The model generalizes fairly well to variations in liquids, container shapes and to severe background noise. All samples are sourced from YouTube with IDs provided. We recommend the reader to try out such examples in the online demo. uz7…
Figure 14
Figure 14. Figure 14: Generalization to music. Qualitatively, we find surprisingly reasonable generalization to flute sounds likely since the same underlying physical phenomenon produces resonance. We do not find generalization to other musical instruments or polyphonic music due to the la…
Figure 15
Figure 15. Figure 15: Failure cases. (a) The model struggles in cases of hemispherical containers that have too much room for air to pass leading to very weak resonance (b) another challenging case is that of bottle-neck containers that show more than one mode in the frequency distribution…
Figure 16
Figure 16. Figure 16: Examples of synthetic sounds of pouring. Each synthetic sample is conditioned on a real sample and a random pitch profile. The cyan curve is the fundamental of axial resonance and the yellow curve is that of radial resonance. Note that while we only use axial resonanc…
Figure 17
Figure 17. Figure 17: Obtaining pseudo labels for visual pre-training. For a given video (sample frame at time t in (a)), we mask out the container (b) and then compute pixel wise differences which leads to a tensor of size F × H × W. We average across width and get a temporal difference m…
Figure 18
Figure 18. Figure 18: Qualitative result for visual pre-training. Video model predictions (blue) of height of liquid with pseudo-ground truth (green) on an example from the test set I. Verifying scale factor computation. As shown in Eq. (11), the theoretical estimate of scale factors is gi…
Figure 19
Figure 19. Figure 19: Estimated scale factors for a subset of containers. Generally, larger containers (e.g., containers 1 and 4) have smaller scale factors since the camera needs to be placed further apart to produce an image where the container is roughly at the center. This is indeed th…
Figure 20
Figure 20. Figure 20: Cross-container generalization in liquid mass estimation. On the dataset by Wilson et al. [96], on the seven container-liquid cases, we train to detect liquid mass on pouring sounds of a single container and test on those of every container. We find promising generali…

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.