This simulator places a primary disturbance speaker and a secondary control driver at opposite ends of a duct. Adjust the tone frequency, the secondary amplitude ratio, extra phase error, controller delay and the error-microphone offset, and watch the two waves sum to a residual that can reach complete cancellation only at the design point.
• A 3D duct with a primary disturbance speaker on one side, a secondary control driver on the other, a phase and amplitude controller and a movable error microphone inside an interference field. • Controls for tone frequency, secondary amplitude ratio, additional phase error, secondary delay and microphone offset from the design point. • Six readouts: residual amplitude ratio, reduction with a 120 dB display ceiling, relative phase at the microphone, and the primary, secondary and summed instantaneous pressures. • Curves & measurements with equations, two guided experiments and a verification bench, and a Learn & assess tab.
The primary wave is p = cos(ωt − kx) and the secondary wave is g cos(ωt + kx + π + φerror − ωτ), where g is the amplitude ratio and τ the delay. At the microphone the relative phase is θ = π + φerror − 2πfτ + 2kx, and the residual amplitude ratio is R = |1 + g e^{jθ}|. Reduction is −20 log10 of that ratio.
Perfect cancellation needs g = 1 and θ = π together. A wrong phase of 180° makes the waves add, doubling the amplitude for a reduction of −6.02 dB, and moving the microphone changes 2kx so the cancellation zone is localized rather than global.
This is two coherent ideal plane waves in normalized pressure with a fixed tone. It has no adaptive filter convergence, no broadband noise and no controller latency beyond the delay you enter. The 120 dB figure simply stands for exact analytical cancellation. Real systems such as headphone or duct ANC must estimate and track the path continuously, which this demonstration deliberately omits.
A secondary source emits a wave with the same amplitude and opposite phase to the unwanted tone, so the two sum to nearly zero at the target location. The simulator shows this with a primary speaker, a control driver and an error microphone.
The waves no longer oppose each other. At a 180° error the secondary wave adds to the primary, doubling the amplitude and giving a reduction of −6.02 dB instead of cancellation.
The relative phase depends on position through the term 2kx. Away from the design point the waves drift out of exact opposition, so the residual grows as the microphone is moved.
Yes. A delay τ shifts phase by 2πfτ, so the same delay produces a larger phase error at higher tone frequencies. The Secondary delay control lets you see this directly.