Auditorium Acoustics: The Best Seat in the House

Research Day Poster April 17, 2007
By: David Grunberg
Advisor: Dr. Youngmoo Kim

The Best Seat in the House

The Problem

In any enclosed space there is sound distortion due to the particular characteristics of the room. Certain frequencies, called resonance frequencies, are amplified much more than other frequencies and can severely distort sound. We decided to investigate the characteristics of Mitchell Auditorium in the Bossone Research Center, particularly focusing on the resonance frequencies, so that we could determine where sound was distorted the least.

William F. Mitchell Auditorium

The Procedure

First, we took measurements at various locations in Mitchell Auditorium. We popped balloons to simulate an impulse source and recorded the resulting waveforms at these locations. Next, we used recordings taken at the point of balloon popping and compared them to the others to determine if the recordings were in sync. We then formed spectrograms and spectrums of the data in MATLAB to examine how smooth the decay progression was and what, if any, resonance frequencies were shown.

Left: a waveform of a balloon, both at the position where it was popped and further back in the auditorium. The further back recording (green) is delayed by a fraction of a second, confirming that the recordings are in sync. Right: a spectrogram of a balloon popping. The smooth curve indicates that resonance is not strong at this position for this recording.

The Results

Using the waveforms we verified that the recordings were indeed in sync. We then estimated the room resonance frequencies, finding that there is one at about 1.5 kHz and another at about 9 kHz. We finally determined that the sound distortion in the auditorium is:
▪ Strongest directly in front of the stage
▪ Weaker to the right and left of the stage
▪ Minimal in the wings at a moderate or significant distance from the stage.

Spectra of the collected data, ordered from worst t best. The smoother the curve, the less resonance and noise in that position. The leftmost spectrum is directly in front of the stage, the middle one is halfway back and to the left of the stage (facing the stage), and the rightmost one is halfway back and to the right of the stage.

Future Work

In order to further determine the acoustic characteristics of Mitchell Auditorium, more readings should be taken with the equipment calibrated carefully enough to measure absolute amplitude levels in the auditorium. It could then be determined where sounds are strongest in the auditorium.