## 3 Experimental Results  
In this experiment, each live horse mackerel was determined to be in good condition during the experiments. Figure 2 shows the received voltage signals (top), _RLs_ (middle), and histogram (bottom) of mean _RLs_ of the direct path of Exp2 (only net, without fish), Exp3 (100 ind. fish in the net cage), Exp5 (300 ind. fish in the net cage), and Exp7 (500 ind. fish in the net cage) at 3 kHz. The blue and red areas show the received signals from the direct and surface paths, and their time intervals were 3.5-4.5 and 5.5-6.5 ms, respectively. The red lines of _RL_ show the local minimum values.  
Figure 2: Representative attenuation experimental results of (**a**) Exp2 (only net, fish without in the net cage), (**b**) Exp3 (100 ind. fish in the net cage), (**c**) Exp5 (300 ind. fish in the net cage), and (**d**) Exp7 (500 ind. fish in the net cage) at 3 kHz; the top figures are the received voltage signals, middle ones are received levels (_RLs_), and bottom ones are the histogram of the _RLs_ from the direct paths. The transmission losses in seawater were compensated for the _RLs_.  
As a result, the direct and surface paths were fully separated. The received voltage signals of the direct path were approximately 0.32, 0.16, 0.1, and 0.07 V in Exp2, Exp3, Exp5, and Exp7, respectively (Figure 2, top). The signals from the direct paths decreased as the number of individual fish increased. For all 100-300 pings acquired in experiments, the \(RL\)s were averaged for comparative analysis. The mean \(RL\)s of the cumulative sum from the direct paths were 187.0 (Exp2), 181.0 (Exp3), 176.3 (Exp5), and 174.3 dB (Exp7) (Figure 2, middle). The standard deviations (std) were 1.3-1.4 dB, and standard errors (SE) were 0.08-0.14 dB. The histograms from all mean \(RL\)s showed the Gaussian distribution (Figure 2, bottom). The \(RL\)s of all pings changed slightly in Exp2, but those of Exp7 fluctuated at 10 dB. The signals from the surface path varied with waves and the passing ship. The \(RL\)s from the direct path were less affected compared with those from the surface path. The \(RL\) of surface paths in all experiments was about 180 dB. However, the surface path was not analyzed because this work focused on the effect of attenuation on the direct path.  
Figure 3 indicates the measured mean \(\alpha\) and maximum \(\alpha\), which were dependent on the frequency and number of individual fish. The mean \(\alpha\) linearly increased with the number of individual fish at the relatively low frequency of 3-4 kHz. At 3 kHz, the mean \(\alpha\) and maximum \(\alpha\) were 6.0 and 6.5, 8.3 and 9.5, 10.7 and 11.7, 12.9 and 15.1, and 13.8 and 14.6 dB/m at 100, 200, 300, 400, and 500 ind., respectively. The ranges of mean \(\alpha\) and maximum \(\alpha\) for all frequencies were approximately 6.0-15.4 dB/m and 6.5-21.8 dB/m, respectively. At a low number of individual fish below 400 ind., the mean \(\alpha\) and maximum \(\alpha\) increased with frequency. At a high number of 400 ind. and 500 ind., the mean and maximum \(\alpha\) and their variation with the number of individual fish peaked at 4 kHz. The mean and maximum \(\alpha\) did not linearly increase at 6-7 kHz and high density of fish (400-500 ind.). The attenuation variation with the number of individual fish was small at such high frequencies (6-7 kHz).