The Whispering Gallery Wave · AI Generator #GEN-0C99F173
Physics
Problem
In a circular whispering gallery of radius R=25.0m, sound waves can travel around the curved wall by repeatedly reflecting off the surface. An acoustic engineer discovers that when she creates a sharp sound pulse at one point on the wall, the returning echoes exhibit a peculiar interference pattern.
The pulse travels around the gallery in both directions (clockwise and counterclockwise) and returns to the starting point. However, due to small irregularities in the wall, the clockwise path is slightly longer: the effective path length is (2πR+ΔL) where ΔL=0.12m.
When the two returning pulses interfere, they create a standing wave pattern with nodes at specific frequencies. The engineer measures that the first node (minimum in the interference pattern) occurs when the original pulse has a frequency of f1=22.0Hz.
Find the speed of sound in the gallery. Assume the speed of sound is constant and that reflections preserve the phase of the waves.