This function computes the resonant and cutoff frequencies when recording in a given aquarium according to the criteria explained in Akamatsu et al. (2002)
akamatsu(Lx, Ly, Lz, mode = c(1,1,1),
c = 148000, plot = FALSE, xlab = "Frequency (kHz)",
ylab = "Attenuation distance (cm)", ...)A list of two items:
Resonant frequency (in Hz). See Details
Cut frequency (in Hz). See Details
watertank length (in cm).
watertank width (in cm).
watertank height (in cm).
mode, see details.
sound velocity in cm/s (by default 148000 cm/s in water).
logical, if TRUE plots the attenuation distance in function of frequency.
title of the x axis if plot is TRUE.
title of the y axis if plot is TRUE.
other plot graphical parameters.
Camille Desjonqueres
From Akamatsu et al. (2002):
1. Resonant frequency
The calculated resonant frequencies of a rectangular glass tank with the dimension of Lx , Ly , and Lz (in centimeters) can
be described by the following equation:
$$f^{rectangular}_{lmn} = \frac{c}{2} \times \sqrt{\left(\frac{l}{L_{x}}\right)^2 + \left(\frac{m}{L_{y}}\right)^2 + \left(\frac{n}{L_{z}}\right)^2}$$
where c is the sound velocity (cm/s) and each l, m, n reprents an
integer, and the combination of these paramameters designates the
'mode number'. The mode (1, 1, 1) represents the resonance wave of minimum
frequency. The mode (2, 1, 1) represents one of the higher order of
resonant component and has additional node of the soundpressure level
at the middle of the X axis, i.e., Lx/2.
2. Cutoff frequency
The cutoff frequency can be calculated as follows:
$$f^{rectangular}_{cutoff} = \frac{c}{2} \times \sqrt{
\left(\frac{1}{L_{y}}\right)^2 + \left(\frac{1}{L_{z}}\right)^2}$$
3. Attenuation distance
The theoretical attenuation distance D can be expressed in function of the
cutoff frequency and the projected frequency following:
$$D^{rectangular}(f) = 2 \times log_{10} \times \frac{c}{4 \pi
f^{rectangular}_{cutoff}} \times \frac{1}{\sqrt{1-\left(\frac{f}{f^{rectangular}_{cutoff}}\right)^2}}$$
Akamatsu T, Okumura T, Novarini N, Yan HY (2002) Emprical refinements applicable to the recording of fish sounds in small tanks. Journal of the Acoustical Society of America, 112, 3073-3082.