Solution to Pesky Bugs

by Andrew Thomas

The wav file included in this puzzle is represents the sound made by six bugs simultaneously flying around the head of a hypothetical listener. The task is then essentially to apply signal processing (or just excellent aural perception) to the file to separate the bug's sounds and determine their path.

Each bug emits a constant-amplitude sine wave tone at an integer multiple of 220 Hz. Each bug also moves at a constant speed, with infinite acceleration to change direction.

The WAV file includes both doppler shifts and amplitude changes as appropriate to the distance to each ear. Several of our testers had difficulty with the following point of acoustical physics: while sound intensity (energy) is inversely proportional to the square of the distance to its source, acoustic pressure (amplitude, the signal which is represented in a sound file such as WAV which uses LPCM) is inverserly proportional to the distance itself. See Wikipedia's Sound Pressure article for more details. This information is key if attempting to work out the bug's position via trilateralization.

The paths described thereby look like this:

where the 6 paths have been horizontally displaced to be easier to see (lowest frequency on the left, highest on the right), and the locations of the listener's ears for each letter are marked with x's.

Thus, the answer is PLAGUE.