I recently visited Echo Amphitheater, a naturally formed amphitheater near Abuiquiu, New Mexico. Despite being central to wild west folklore, the site has never (to my knowledge) been studied for its acoustical properties. To gain a better sense of the exotic acoustics of the amphitheater, I recorded myself clapping my hands four times with a TASCAM DR-05 field recorder. When I returned to Dallas, I analyzed the echo, decay, and bandpass of the amphitheater to study its size, shape, and composition.
Table of Contents
Below are the four handclaps. Feel free to download, share, analyze, etc.
The annotated waveforms below identify the first four echoes and indicate their order.
In the table below, the time between each echo from the previous echo is recorded. The initial clap is set at t = 0.
|Clap #||1st order echo time (s)||2nd order echo time (s)||3rd order echo time (s)||4th order echo time (s)|
We can learn more about the size and geometry of the Echo Amphitheater by considering the speed of sound (v ≃ 343 m/s).
Now considering that the distance traveled l = vt,
The path defined by the lengths lb, ld, and lf can help us find the curvature of the canyon. We have two ways to find the lengths (depending on the experimental setup):
If we set up the microphone and source near the center of the amphitheater wall, lb ≃ lc, ld ≃ le, and lf ≃ lg. The above system of undetermined equations then becomes determined:
If we set up the microphone and source a good distance away from the amphitheater wall (la ≃ lc ≃ le ≃ lg), the above system of undetermined equations becomes determined:
We can find the decay factor (measured in dB per echo order) of the canyon by analyzing the intensity of the initial claps and the first-third-order echoes (the fourth order echo was too faint to accurately measure the intensity). The decay factor is average of the slope of the graphs below.
The decay factor was calculated to be -12.225 dB/echo order. The decay factor is a reflection of the canyon's composition. You can read about the geological history of the Echo Amphitheater here.
In addition to modulating the delay and amplitude of the input signal, and the amphitheater modulates the spectrum, acting as a low-pass filter. This can be seen below:
Since the peak of the initial clap was around 1000 Hz, the bandwidth (BW) is about three octaves:
We see a similar ~three octave bandwidth (BW) for claps 2-4:
We can quantify this calculate low-pass effect with the so-called Q-factor: