Make a quiet spot. Add sound.: sources & model

Open a headphone, line up two pressure changes, then keep your setting while the sound changes. Discover why timing, microphones and location matter—and inspect a real measured acoustic path.

What supports the explanation?

What this model assumes

1. The original over-ear geometry is a generic functional cutaway, not a manufacturer scan, exact teardown or measured ear-canal model.
2. Driver motion is enlarged and slowed to show activity. Geometry, cushion fit and control mode do not generate a fabricated product attenuation curve.
3. Pressure traces are normalized small-signal variations. Relative levels are not dB SPL, perceived loudness, exposure estimates or hearing tests.
4. The tone, spatial strip and arrival race are separate declared models. They do not implement adaptive filtering, a full room, live microphone feedback or a retail ANC algorithm.
5. The spatial sources stay fixed while the probe moves. Moving a head with a worn headphone is a different situation.
6. Exact ideal cancellation has real-world limits absent from this calculation. Early signal arrival establishes only a timing opportunity.
7. The actual QC25 photograph, modified QC20 measurement and original generic cutaway are three different references.
8. Consumer ANC alone does not establish suitable hearing protection. Product rating, fit and exposure matter.
9. A stated phase convention: The added pressure is g cos(2πft + θ − 2πfτ). Here θ is its actual phase before the explicit delay τ. The original pressure is cos(2πft). At gain g = 1, delay 0 and θ = 180°, their sum is ideally zero.
10. Add pressures before calculating their level: The residual-to-original amplitude ratio is R = √(1 + g² + 2g cos(θ − 2πfτ)). Equal-frequency correlated pressures must be added before squaring. Adding their separate dB values would give the wrong result.
11. Relative dB is not a loudness percentage: For this single-frequency comparison, the change is 20 log₁₀ R. With correct opposition and gain 0.8, R = 0.2, or about −13.98 dB relative pressure. That is not a claim of 80% less perceived loudness. Exact zero is shown explicitly, not mislabeled 0 dB.
12. One delay, several outcomes: With gain 1, phase 180° and delay 0.25 ms, the model gives about −16.09 dB at 100 Hz, −2.32 dB at 500 Hz, +3.01 dB at 1000 Hz and +6.02 dB at 2000 Hz. These are analytic examples, not the response curve of a retail headphone.
13. Two components do not average in decibels: For equal-amplitude 100 Hz and 1000 Hz components, average their mean-square contributions over common complete cycles. At the quarter-millisecond setting, their combined change is about +0.053 dB. Strong bass reduction does not guarantee a reduction of the total.
14. A defined spatial model: Two equal-amplitude plane waves travel in opposite directions. With cancellation tuned at x₀, the residual amplitude ratio is 2|sin(2πf(x − x₀)/c)|. We fix c = 343 m/s as an illustrative value. Nodes repeat at half-wavelength intervals; this is not a universal spherical quiet bubble.
15. Shorter wavelength, narrower node region: Around a node, the region with at least 10 dB pressure reduction has half-width λ/(2π) asin(10^(−10/20)/2). It is about 8.67 cm at 100 Hz and 0.867 cm at 1000 Hz in this particular geometry. Those are model dimensions, not measured headphone fit tolerances.
16. A causal budget includes the acoustic leg: For our authored example, noise travels 30 mm in 87.46 microseconds. Secondary sound travels 10 mm in 29.15 microseconds. That leaves 58.31 microseconds for processing. A 40-microsecond delay can arrive early; an 80-microsecond delay arrives about 21.69 microseconds late. Early arrival alone does not prove a correct filter.
17. Feedforward, feedback and hybrid: Feedforward uses reference information, often sensed outside. Feedback uses a residual measurement, often inside. Hybrid architectures combine information. Designs vary, and a microphone’s response need not equal the response at the eardrum.
18. Why flipping every sample is insufficient: Using the additive convention e = d + S·y, with d = P·x and y = W·x, formal cancellation suggests W = −P/S wherever defined. A usable controller must also address causality, stability, conditioning, limits and changing paths. The ratio is not a ready-to-run safe controller.
19. A measured path is one part of the system: PANDAR’s modified QC20 hardware had the original Bose ANC electronics removed. One stored record has 8,192 samples at 48 kHz per channel. Its preprocessed coefficients retain the electronic backend here and have unspecified stored units. They are not a noise recording, pressure in pascals, hearing sensitivity or achieved cancellation.
20. Pressure nodes do not account for all energy: This lesson calculates pressure superposition. It does not calculate the complete pressure/particle-velocity energy flow. A node is not evidence that acoustic energy or the outside source vanished everywhere.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Original generic ANC headphone cutaway, rendered from the actual interactive model. Authored functional geometry, not manufacturer CAD or measured acoustic performance.