seewave (version 1.7.6)

akamatsu: Water tank minimum resonant and cutoff frequencies

Description

This function computes the resonant and cutoff frequencies when recording in a given aquarium according to the criteria explained in Akamatsu et al. (2002)

Usage

akamatsu(Lx, Ly, Lz, mode = c(1,1,1),
         c = 148000,  plot = FALSE, xlab = "Frequency (kHz)",
         ylab = "Attenuation distance (cm)", ...)

Arguments

Lx

watertank length (in cm).

Ly

watertank width (in cm).

Lz

watertank height (in cm).

mode

mode, see details.

c

sound velocity in cm/s (by default 148000 cm/s in water).

plot

logical, if TRUE plots the attenuation distance in function of frequency.

xlab

title of the x axis if plot is TRUE.

ylab

title of the y axis if plot is TRUE.

...

other plot graphical parameters.

Value

• A list of two items:
• res
  Resonant frequency (in Hz). See Details
• cut
  Cut frequency (in Hz). See Details

Details

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: $$D^{rectangular}(f) = 2 \times log_{10} \times \frac{c}{4 \pi f^{rectangular}_{cutoff}} \times \frac{1}{\sqrt{1-\left(\frac{f}{f^{rectangular}_{cutoff}}\right)^2}}$$

References

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.

Examples

akamatsu(60, 30, 40)