The voice of a freezing lake

That is how long the whole model record lasts. For the first approx. 1.3 s the signal exceeds 1% of its maximum; then it fades, and it is exactly zero only after 1.63 s. Choose a fragment — it will unfold below. This is a synthesis, not a recording; the sound does not tell you whether the ice is safe.

below 1% of maximum

A model diagram, not a recording. Axis: 0–3 s. The band shows the highest and lowest value in each 5 ms segment; white — direct pulse, violet — echo. Amplitude units are arbitrary. The rectangle is the zoom window. Dashed line: beyond it the signal is weaker than 1% of the drawing's maximum, but not yet exactly zero; exact zero comes only after 1.63 s. Without JavaScript you see only a hand-drawn illustrative diagram, not a computed plot.

Window width: 30ms

Close-up: Front

window 0.295–0.325 s

direct pulse echo (×0.38) grey band: what of this fragment is visible in the full view. Axis: time from the start of the record, ms. The same signal, only at a different scale. show band

The close-ups require JavaScript. Below, in section 01, the four fragments of the record (front, middle, tail, echo) are described in plain text.

Window 0.295–0.325 s.

Playback only on request. This is a synthesis from the model, not a recording.

Four close-ups in words

A description for the model's default settings. It works without JavaScript, without the plot and without sound.

Front window 0.295–0.325 s

Before 0.300 s the model is silent (zero in the model, not a missing measurement). Then the highest component enters, 1500 Hz; one oscillation lasts 0.67 ms.

Middle window approx. 0.50–0.53 s

The higher components are already dying away, while the lower ones are only just arriving. At the middle of the window the component with the largest envelope is 990 Hz (period 1.01 ms).

Tail window 0.724–0.784 s

The last, lowest component enters: 310 Hz, period 3.23 ms. These are the slowest and longest oscillations in the record.

Echo window 0.645–0.705 s

Violet is the same sequence after 0.35 s, weakened to 38% of the amplitude. It starts at 1500 Hz while part of the direct pulse is still ringing out; in playback the two waves add together.

Why the crack stretches out

In the model the pulse is eight pure tones, from 1500 to 310 Hz. They do not arrive at once: each subsequent, lower one lags by approx. 61 ms (with the default settings the delays fall between 0.300 and 0.729 s). Instead of a single crack, a descending series of bursts appears. This is dispersion: tones of different frequencies arrive at different times.

The smooth outline visible in the full view is the silhouette of these oscillations. The close-up shows what that silhouette is made of — nothing in the signal changes, only the scale does.

According to source [1] (kept from V2, not opened in this run), the sounds of ice are linked to temperature changes and deformation of the ice cover. According to source [2], dispersion depends, among other things, on the structure of the medium. The delays in this model are a simple linear ladder, not a calculation for any real lake.

What this synthesis does not say

This is neither a recording nor a measurement. We have no ice thickness, temperature or location.

The sound — or its absence — does not tell you whether it is safe to walk on the ice. Nobody here steps onto the ice: we are listening to a model.

The parameters (path, dispersion, echo delay) are arbitrary and are not calibrated to any ice cover. The decay of each component is a model constant, not a measurement of attenuation by snow or water.

The echo is the same sequence, delayed and weakened, without any additional dispersion from a longer path. This simplification needs to be checked by an acoustician.

A field recording with a licence and a description of how it was made is missing. A photograph of a lake would not authenticate the synthesis, which is why there is none here.

Technical appendix: how the record was drawn

The full view divides 3 s into 600 segments of 5 ms each. In each, the model is computed every 0.0625 ms (at least 10 samples per period of the fastest component, 1500 Hz), and the highest and lowest values are drawn. If only sparse, evenly spaced points were drawn, the fast oscillations would blur into a false, slower shape (aliasing). The 30–60 ms close-ups are drawn from 1200 points (at least 13 samples per period of 1500 Hz).

The vertical scale of the close-up is fitted to the fragment; the magnification relative to the full view is given in the label next to the time scale.

f_k = 1500 − 170·k Hz, k = 0…7 · t_k = t₀ + Δ·k/7 · t₀ = 0.12 + 0.003·path s · Δ = 0.006·dispersion·(0.5 + path/100) s · g = 0.575 (constant amplitude scale) ·τ_k = t − t_k, 0 ≤ τ_k < 0.55 s · s(t) = g/8 · Σ sin(2π·f_k·τ_k) · e^−18τ · (1 − e^−140τ) · echo = 0.38 · s(t − t_echo). Amplitude in arbitrary units; “path” and “dispersion” are dimensionless values 0–100.

Default values: path 60, dispersion 65, echo after 0.35 s; g = 0.575 is the value that V2 gave at attenuation 30. The formulas were kept from V2; their physical correctness is for an acoustician to judge.