CA06 exercise · Geometrical-acoustics exercise
Construct direct and first-order reflected paths in a rectangular room, compute arrival times and estimate simple early-energy room-acoustic descriptors.
Aim
You will construct direct and first-order reflection paths in a rectangular room and convert geometric path lengths into arrival times and simple energy indicators.
Use a 2D room with dimensions 8 m × 5 m, source at (2.0, 2.0) m and receiver at (6.5, 3.2) m. The direct path is the line from source to receiver. A first-order reflection is represented by one mirrored source.
In a rectangular room the first reflections are easy to construct. In general rooms an image source must pass an audibility test: the reflection point must lie on the real surface and the path must not be blocked.
What is a main limitation of a pure ray-energy model?
Python exercise
The code prints direct/reflected arrival times, plots the image sources and builds a simple time-energy response for C80/D80 interpretation.
Expected observation
Direct sound arrives first; first reflections arrive later. Changing absorption changes the early/late energy balance.
Teaching note
This exercise prepares students for room-acoustic ray tracing and interpretation of early reflections.
Written submission
When would you avoid pure geometrical acoustics?
Give one acoustic situation where you would prefer FEM/BEM/modal analysis instead of pure ray tracing.
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