Schaeffer and Oliver Shape, volume, and resonance frequency of the swimbladder of Thunnus albacares 



369 



fer's (1999) is shown in Figure 6. The rela- 

 tionship is well described by a power function 

 fitted to the nontransformed data by means of 

 a weighted regression procedure: 



y,. = 0.00000002 .r^ "601, (7-^'=0.83, « = 108 (4) 



([fish length range: 

 353 to 1569 mm]) 



where V,. = a swimbladder volume at fish length .v. 



The weighting employed consisted of the 

 reciprocal of the variance about the volumes 

 within each 200-mm length interval. 



Swimbladder resonance frequency 



The monopole-dominant resonance frequency 

 of a swimbladder (Andreeva, 1964) is approxi- 

 mated by using a spherical volume of gas (Love, 

 1978) as follows: 



Resonance frequency 



STP 



(5) 



where T = 1.4; 



r = radii of equivalent sphere in 



meters; 

 Z) = density of fish flesh (1050 kg/m-'); 



and 

 P = sound speed parameter at depth Z 



defined as 



P- 



1 + 



10„ 



X 10100 Pascals. (6) 



Because yellowfin tuna swimbladders are not 

 spherical, the predicted resonance frequency 

 must be adjusted to account for the approxi- 

 mate prolate spheroid shape of the swimblad- 

 der (Figs. 1 and 2). Weston ( 1967) has provided 

 a formula and figi.n'e (Chap. 5, p 59, Fig. 

 5.2) for this adjustment using the ratio of the 

 swimbladders maximum (a) and minimum (b) 

 radii (e.g. 1/2 length and 1/2 width). From the 

 figure, we interpolated the magnitude of the 

 upward adjustment at various depths, incorpo- 

 rating Boyle's Law to account for changes in 

 volume with depth. The swimbladder's maxi- 

 mum radius (a) was held constant at all depths 

 because it is firmly attached to the connective 

 tissue sheet adjacent to the dorsal wall of the 

 abdominal cavity. We calculated the expected 

 minimum radii (b) at various depths, using the 

 predictive regression function for swimbladder 



