Active Noise Cancellation: How Anti-Sound Eliminates Noise

simulator intermediate ~10 min
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NR = 25.2 dB — 94.5% reduction

With 5° phase error and 5% amplitude mismatch, the ANC system reduces a 200 Hz, 70 dB noise by 25.2 dB — from clearly audible to a whisper.

Formula

A_residual = sqrt(An² + Ac² + 2×An×Ac×cos(π + Δφ)) (vector sum)
NR = 20 × log10(An / A_residual) dB
Efficiency = (1 - A_residual / An) × 100%

Silence Through Sound

Active noise cancellation exploits a fundamental property of waves: superposition. When two waves of equal amplitude meet in opposite phase (180° apart), they destructively interfere and cancel each other. By generating a precise anti-phase copy of unwanted noise and playing it through a speaker, ANC systems can dramatically reduce ambient sound — turning a noisy airplane cabin into near-silence.

The Physics of Cancellation

Perfect cancellation requires the anti-noise to match the original noise exactly in frequency, amplitude, and arrive precisely 180° out of phase. Any mismatch reduces effectiveness. The residual sound after cancellation follows vector addition: A_residual = sqrt(An² + Ac² + 2AnAc·cos(phase_difference)). This simulation lets you explore how phase errors and amplitude mismatches degrade cancellation performance.

Engineering Challenges

Real ANC systems face formidable challenges. The noise must be sensed, processed, and the anti-noise generated with latency under 1 millisecond. Broadband noise requires adaptive filters (typically LMS algorithms) that continuously adjust to the changing noise spectrum. Multiple noise sources from different directions create a complex sound field that a single speaker-microphone pair cannot fully cancel.

Modern Applications

ANC has evolved from laboratory curiosity to ubiquitous consumer technology. Premium headphones achieve 20-30 dB noise reduction, transforming air travel comfort. Automotive ANC reduces engine and road noise in car cabins. Industrial applications include silencing HVAC ducts, transformer hum, and MRI scanner noise. Future applications may include quiet zones in open-plan offices and active window noise barriers.

FAQ

How does active noise cancellation work?

ANC uses a microphone to detect incoming noise, processes the signal to generate an anti-phase (inverted) copy, and plays it through a speaker. When the anti-noise meets the original noise, destructive interference cancels the sound. The key challenge is matching phase and amplitude precisely in real time.

Why is ANC better at low frequencies?

Low-frequency sounds have long wavelengths, so small timing errors cause minimal phase mismatch. High-frequency sounds have short wavelengths — even microsecond delays create significant phase errors. Most ANC headphones effectively cancel below 500 Hz but rely on passive isolation for higher frequencies.

What limits ANC performance?

Phase accuracy, amplitude matching, latency (processing delay), and the complexity of the noise field all limit performance. Broadband noise is harder to cancel than tonal noise. Multiple noise sources from different directions require more sophisticated multi-channel systems.

What is feedforward vs feedback ANC?

Feedforward ANC places the microphone outside the ear cup to detect noise before it arrives, allowing pre-computation. Feedback ANC places the microphone inside the ear cup to measure the residual error signal. Most modern headphones use hybrid systems combining both approaches.

Sources

Embed

<iframe src="https://homo-deus.com/lab/acoustics/noise-cancellation/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub