Image Source Theory

Each hard wall spawns a mirror-image "ghost" speaker; the audience hears the direct sound first, then the reflection arriving later and from a different angle.

What it is

A method that models each wall reflection as sound coming from an imaginary mirror-image copy of the speaker behind that wall.

Key facts

• Speed of sound in air ≈ 343 m/s at 20 degrees C (rises ~0.6 m/s per +1 degree C).
• Delay = extra path length (m) ÷ 343. Example: 4 m extra = 11.7 milliseconds late.
• Sound travels ~34.3 cm per millisecond, so 1 ms of delay ≈ 0.343 m of extra path.
• Doubling distance from a point source drops level by 6 dB (inverse-square law).
• Halving power = -3 dB; -3 dB is the half-power point, -10 dB sounds about half as loud.
• Reflection energy = direct energy x (1 - alpha), where alpha = absorption coefficient (0 = total reflect, 1 = total absorb).
• Hard surfaces: painted concrete alpha ~0.02, glass ~0.03, plasterboard ~0.05; soft: heavy curtain ~0.5, 50 mm foam ~0.8.
• Haas / precedence effect: a reflection 1-35 ms late fuses with the direct sound (no echo) but pulls image location toward the first arrival.
• Reflection later than ~50 ms (about 17 m extra path) is perceived as a separate echo.
• Direct + reflection of equal level create comb filtering: first cancellation notch at f = 1 / (2 x delay) Hz, e.g. 1 ms delay = 500 Hz notch.

How it works

1. Treat each flat hard surface as a mirror.
2. Place an imaginary copy of the speaker the same distance on the far side of that wall.
3. Draw a straight line from the image speaker to the listener; where it crosses the wall is the reflection point.
4. The extra path length = image distance minus direct distance; divide by 343 m/s for the delay.
5. Drop the reflection's level by the surface's absorption and by distance (inverse-square).
6. Add every image source up to predict the full early-reflection pattern.

Real examples

• Speaker 2 m from a side wall: the image speaker sits 2 m behind it, so the reflection travels ~4 m extra and lands ~11.7 ms late.
• Concrete brick wall (absorption ~0.02) reflects ~98% of energy back as a slap-back image; heavy curtain (~0.5) kills half of it.
• A reflection arriving >50 ms after the direct sound (path ~17 m longer) is heard as a distinct echo, not just colouration.
• Two parallel hard walls create infinite image speakers bouncing back and forth = flutter echo (that 'boing' clap).
• Aim a tweeter at a glass window 3 m away and the ghost speaker fires a bright slap-back straight at the front rows.

How it helps in live sound

• Walk the room and find the parallel hard walls/glass first; those are your worst image sources for slap-back.
• Toe speakers IN (aim across the audience, not parallel to side walls) to throw reflections into absorption, not the crowd.
• Use a measurement mic + REW/Smaart impulse response: early spikes after the direct peak ARE the image sources, read their ms delay.
• Hang drape or 50 mm absorption on the first reflection point (mirror trick: where a helper sees the speaker in a mirror on the wall).
• Keep direct-to-reflection gap under 35 ms to stay inside the Haas window so it tightens imaging instead of echoing.
• Pull the rig 1-2 m off back/side walls; every metre off the wall adds ~6 ms and softens the slap.