#sound waves

In an ordinary laboratory the mean temperature is the first environmental variable that is deliberately fixed—typically near 25 °C by thermostats and the thermal mass of the room. Once that average temperature is clamped, the most consistent thermodynamic idealization is the non-adiabatic (isothermal) limit: dT=0 and therefore dT/T=0. All subsequent analysis of sound propagation is performed under this single, laboratory-motivated constraint.

The subtlety that links dT=0 to sound propagation With temperature held rigorously constant the ideal-gas law collapses to Boyle’s relation p ∝ ρ. A sound wave then consists solely of a pressure–density oscillation; there is no accompanying temperature ripple. The local propagation speed cT= sqrt (p/ρc) is therefore amplitude-independent at the thermodynamic level. The only remaining source of non-linearity is kinematic: the fluid particles themselves advect the wave, so that the exact characteristic speed becomes u+cT. Because the particle velocity (u) scales directly with the relative pressure amplitude r=dp/pm, the size of this convective correction is simply (r). Consequently, the entire question of whether a sound wave remains a “subtle” perturbation on equilibrium reduces to how small (r) stays.

Scan from 0 dB to 160 dB A systematic sweep of relative amplitude from the threshold of hearing (r≈2×10^−10 at 0 dB) to 160 dB (r≈0.02) maps the practical domain of human and laboratory acoustics. Up to ordinary conversation and even the onset of discomfort the relative quadratic term remains orders of magnitude below 0.1 %. Only when the level reaches the extreme high-intensity regime does the kinematic correction become measurable. The scan is therefore relevant in two complementary ways: it quantifies how profoundly linear everyday sound is under a fixed-temperature constraint, and it identifies the amplitude at which that linearity finally fails.

Onset of non-linearity on the plot and its physical meaning

On the higher-resolution semi-log map the local convective term crosses the 0.1 % threshold at approximately 140 dB (r≈2×10^−3). At the same level the theoretical shock-formation distance falls to roughly 80 wavelengths. Physically this marks the point at which crests begin to catch troughs appreciably within laboratory-scale distances: the wave starts to steepen, higher harmonics grow, and the assumption of a fixed, uniform equilibrium begins to erode. Below 140 dB the same mechanisms exist in principle but remain negligible for any realistic path length; above 160 dB they dominate within a few wavelengths and the linearized description collapses.

Scan plot: Higher-resolution maps of local convective non-linearity and cumulative shock-formation distance versus SPL in an isothermal ideal gas. The 0.1 % local threshold and practical laboratory scales are both crossed near 140 dB, marking the onset of clear kinematic non-linearity.

Free-to-air broadcast reaches the widest, most varied audience of any medium — all ages, all technical skill levels, everywhere. That scale means the opt-in and disclosure design has to work for the least technical, most casual viewer, not just power users. Wide reach is the argument for careful consent design, not a reason to route around it.

Two Tiers of Signal — Kept Strictly Separate

Not every signal an audience produces carries the same weight, and the system's design has to reflect that difference rather than flatten it. Two tiers, distinct in sensitivity, disclosure burden, and technical mechanism:

Tier 1 — Passive Engagement Metadata. Collected through a companion or second-screen app: poll responses, watch-time, taps, scroll and attention proxies. This is the lightest-touch layer — low sensitivity, aggregated by default, and requiring only a modest, everyday disclosure. It's the digital equivalent of a viewer raising their hand; nothing about the home itself is sensed, only how someone engages with the content on their own screen.

Tier 2 — Active On-Device Acoustic Sensing. A fundamentally different category: the TV or speaker acts as a sonar emitter, and its own microphone captures the returning echoes to characterize the room's impulse response — motion and presence inferred from how a known emitted signal reflects off the space. This is grounded in real, demonstrated physics (the CovertBand approach: correlating an emitted signal against its own reflections), not speculation. But because it requires a device's microphone to actively listen inside someone's home, it sits in an entirely different sensitivity class than tier 1. It must live in its own clearly labeled consent tier — never folded into a generic "camera/mic" toggle and never enabled by default. If tier 1 is a raised hand, tier 2 is a device listening to the room itself, and it should be disclosed with the weight that distinction deserves.

To-Do, Acoustics development scoped

Consent UI. Write a plain-language disclosure specific to tier 2 — not a buried clause inside a broader privacy policy, but its own clear moment of explanation. Test for comprehension, not just clicks: after opting in, can someone accurately describe what the device is doing? Pair this with an opt-out that works instantly, mid-session, no friction.

Signal collection. Specify precisely what's extracted from the echo data — presence and motion only, or something more granular — and lock that scope down before building anything further. Timestamp every derived signal against the broadcast clock so it can be meaningfully tied to content.

Privacy engineering. Default to aggregation and anonymization; set a firm floor on the smallest group size that can ever be reported, so no output can be traced back to a single household. Periodically audit whether a coarser, less invasive signal could satisfy the same marketing objective — and prefer it when it can.

Studio-side integration. Give producers a real-time dashboard linking engagement and sensing signals to specific broadcast moments, backed by a pipeline stable enough to handle large concurrent audiences without degrading timing accuracy.

Legal. Every implementation must comply with all applicable local and international media, communications, and data-safety laws, and fully respect intellectual property rights, before any feature ships, given the global audience. Build explicit, more conservative handling for any possibility that minors are present. Publish a periodic, plain-language transparency report — what's collected, why, and how to stop or share it.

Success metric. Never report engagement lift on its own. Pair it, every time, with opt-in rate and comprehension rate — a strong engagement number next to a weak comprehension number isn't success, it's a signal that the disclosure failed.

Door left open, explicitly bounded. Future work may explore additional modalities (e.g., on-device optical or RF sensing, if a device already has that hardware) — but only under the same discipline used throughout this scoping: each new modality gets its own hypothesis-testing pass, its own literature anchor, its own explicit consent tier, before any claim is made about what it can do. This line exists to keep the door open to legitimate extension, not to preauthorize a future capability that hasn't been vetted yet.

Conclusion. Built this way, active acoustic sensing is a genuinely interesting and buildable research space — but only as its own clearly disclosed, clearly opted-into layer, sitting alongside (not folded into) ordinary engagement tracking. That structure is what would make the resulting data trustworthy enough for both researchers and audiences to stand behind.

Image: Echo chamber of the Dresden University of Technology.

Sorry about the lack of posting for the past month and a half; I have been taking a break from posting to catch up mentally with myself, experience life a little, and Brainstorm ideas. To demonstrate this catch-up is an older piece of mine from I believe around 1 & 1/2 years past at the point of this post. The piece is a play on the phrase "riding the waves," taking varying sizes of sine, square, and triangle waves to make a semi-pleasing view while experimenting with a little bit of perspective and colours. ---------------------------------------------------------------- A track I will highlight this time that I know I would have listened to during this period of my life is:

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