DEM AudioLinFIR Documentation
LinFIR

Multi-Driver Interference

On this page

When several drivers reproduce the same frequencies, what a listener hears at a given angle is their sum, and that sum depends on when each driver's sound arrives. This page explains why LinFIR's directivity predictions need each measurement's time-of-flight. The analysis itself is described in Directivity Analysis, and the workflow in Preserving Time-of-Flight.

The Physics of Interference

When multiple drivers reproduce the same frequency range, their outputs combine in space. The phase relationship between drivers depends on:

  1. Physical separation between drivers (geometry)
  2. Acoustic path length differences to the measurement point
  3. Crossover filter phase shifts

How Time-of-Flight Encodes It

Each driver's impulse arrives at a slightly different time:

  • This delay represents the acoustic path length to the microphone
  • At the on-axis position, path lengths may be similar
  • At off-axis positions, path length ratios change

Off-axis measurements capture geometry:

  • Driver A might be 1.0 meters away on-axis
  • Driver B might be 1.05 meters away on-axis (5 cm path difference)
  • At +30° off-axis, Driver A might be 0.95 m and Driver B might be 1.15 m (20 cm difference)
  • This changing path length ratio creates interference patterns

These delays create directivity:

  • At some frequencies, drivers sum constructively (in phase)
  • At other frequencies, drivers sum destructively (out of phase)
  • The frequency where this happens depends on the angle (because path lengths change with angle)
  • This is the fundamental physics of directivity

What Happens If Time-of-Flight Is Removed

Time-aligning removes geometric delay information:

  • All drivers appear to arrive at the same time
  • DI calculation assumes drivers are co-located (all at the same point in space)
  • This is physically incorrect for real speakers

Predicted interference patterns don't match reality:

  • Off-axis nulls and peaks won't appear
  • Directivity sonograms show incorrect lobing
  • DI curve does not reflect actual radiation pattern

Example:

With TOF preserved:

  • Tweeter and woofer are 15 cm apart vertically
  • At 2.3 kHz (wavelength ≈ 15 cm), expect null at certain off-axis angles
  • DI curve shows this correctly

With TOF removed (time-aligned):

  • Software thinks drivers are co-located
  • Predicts no null at 2.3 kHz
  • DI curve is smooth (incorrect)
  • Real speaker still has null at 2.3 kHz off-axis