1. The standard deviation of the observed peak frequencies away from the least-squares fit to ω(k)=vϕ k was only 2.1 Hz for frequencies below 3.5 kHz. The phase velocity vϕ of sound was determined from the fit to be 344.79 ± 0.24 m/s in excellent agreement with that calculated using an ideal gas expression for dry air at the measured lab temperature of 22.4 C: 344.72 m/s. See, for example, the HyperPhysics Concepts website of Georgia State University, Speed of Sound: <http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/souspe3.html>.
2. Wikipedia describes several of these methods, e.g., <https://en.wikipedia.org/wiki/Finite_element_method>, <https://en.wikipedia.org/wiki/Method_of_moments_(electromagnetics)_>.
3. In general, the method of images (MOI) enjoys a long history in the computer-aided engineering analysis of room and structural acoustics. Pioneered in a now-classic paper by Allen and Berkley (Ref. 15), it used image sources to estimate the time-domain, reverberation response of a room to a short sound impulse. The resulting reverberation time envelope characterizes the suitability of a space as, for example, a lecture hall or recording studio, a diagnostic introduced in 1895 by W. C. Sabine (Ref. 16). The method does not, however, employ coherent superposition of waves from the source and its reflections, and it is, therefore, unsuitable for frequency response calculations of a cavity whose dimensions are of the order of a wavelength, as in our case. The use of MOI-based calculations of a space's acoustic reverberation response has become a standard of the industry. The Wayverb website, Ref. 17, includes a summary of current techniques employed by several popular acoustic engineering tools: <https://reuk.github.io/wayverb/context.html#existing-software>. All of these tools, however, are inappropriate for the task at hand.