Ray Acoustics

Treating sound like straight beams of light that bounce off surfaces, useful for figuring out where echoes go.

A speaker's high-frequency ray mirrors off a hard wall (angle in = angle out) and lands on the crowd and open mics as an echo.

What it is

Treating sound as straight rays that travel in lines and bounce off hard surfaces like light off a mirror.

Key facts

Speed of sound in air: 343 m/s at 20 degrees C (about 1235 km/h, roughly 1 ft per millisecond)
Speed formula c = 331 + 0.6 x T, where c = speed (m/s) and T = air temperature (degrees C); rises ~0.6 m/s per degree
Law of reflection: angle of incidence = angle of reflection, both measured from the surface normal (the perpendicular)
Ray model is only valid for HIGH frequencies whose wavelength is small vs the surface (roughly above 500 Hz to 2 kHz)
Wavelength lambda = c / f, where lambda = wavelength (m), c = 343 m/s, f = frequency (Hz); 1 kHz = 0.34 m, 10 kHz = 34 mm, 100 Hz = 3.4 m
Inverse-square law: every doubling of distance from a point source drops level by 6 dB (-6 dB per distance doubling)
Direct + reflection can sum to +6 dB (in phase) or cancel toward -infinity (out of phase = comb filtering)
Echo threshold: a distinct echo is heard when the reflection arrives >50 ms after the direct sound (~17 m extra path)
Haas / precedence effect: reflections within ~5-35 ms fuse with the direct sound instead of being heard as a separate echo
Reflection delay (s) = extra path length (m) / 343; e.g. 11.4 m extra path = 33 ms. Hard surfaces (glass, tile, concrete) reflect 95%+

How it works

Picture each speaker firing straight rays outward, like a torch beam.
When a ray hits a hard flat surface, mirror it: bounce angle out equals angle in.
Trace the bounced ray onward to see where the reflection lands.
Measure the bounced path length; divide by 343 m/s to get the echo delay in seconds.
If that delay exceeds ~50 ms, the crowd hears a distinct slap-back echo.
Re-aim, tilt or treat the surface so the troublesome ray misses the audience and mics.

Real examples

Back wall behind the crowd adding ~17 m of extra path versus the direct sound: bounce returns ~50 ms late = audible slap-back on vocals.
Glass shopfront beside an outdoor gig mirrors your top end straight into the open vocal mic = feedback.
Two parallel brick walls in a hall create a flutter-echo 'zing' on hand claps.
Tiled atrium ceiling reflects HF down onto the front rows, making them harsher than the back.
Splaying speakers 10-15 degrees off a side wall stops the reflection landing on the audience.

How it helps in live sound

Walk the room first: every glass, tile, concrete or metal panel is a mirror for your 2-10 kHz.
Aim mains so the on-axis ray hits absorptive bodies (the crowd), not a bare back wall.
Tilt/down-angle tops 3-6 degrees so HF rays die in the audience, not bounce off a hard ceiling.
Keep open mics OUT of the path of any reflected ray to kill feedback before it starts.
Splay or angle PA at least 5-10 degrees off parallel hard walls to break flutter echo.
If a reflection is >17 m of extra path (>50 ms), expect a slap-back: cut level, re-aim, or hang a drape.

Everyday analogy

It's like shining a torch around a room full of mirrors and watching the beam ricochet, except the beam is your PA's high end.

Watch out

Myth: ray acoustics works for all sound. Wrong: it only holds for high frequencies whose wavelength is small vs the surface; bass (long wavelength) bends and diffracts, so rays badly mispredict it.

Fun fact

A reflection that arrives within about 35 ms of the direct sound is not heard as an echo at all: your brain fuses it with the original and even uses it to make the source seem louder (the Haas precedence effect).

Key takeaways

Sound = straight rays that mirror off hard surfaces (angle in = angle out).
Only valid for highs; bass is too long-wavelength and bends instead.
Reflection delay = extra path length divided by 343 m/s.
>50 ms late = audible echo; under ~35 ms = fuses (Haas).
Use it to aim PA away from hard walls and keep reflections off mics.
Direct + reflection can add +6 dB or comb-filter toward cancellation.