Theatre Acoustics
Geometry & Trigonometry
Calculate direct and reflected sound path lengths in a theatre to find which seats hear a clean sound and which hear an echo.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Sound reaching a seat in a theatre travels by more than one path: directly from the stage, and reflected off walls, ceiling and floor. Each path has a different length, so the reflected sound arrives slightly after the direct sound. If that delay is long enough, the audience hears a distinct echo instead of a single blended sound. This exploration asks you to calculate path lengths and delays for real seats in a real auditorium, and to find where the best and worst seats are.
Guiding Questions
- In a theatre, sound reaches you directly and from reflections. Which paths matter most for what you hear?
- Pick a seat and compute the direct and first-reflection path lengths. What is the delay between them?
- Where are the best and worst seats by this measure? Map the delay across the hall.
- Curved ceilings can focus sound. Model a curved reflector and find its hot spots.