(Color online) Histogram of active bubble sizes from a Monte Carlo computer simulation based on about 250 000 randomly drawn active growth stages and random final-stage sizes according to the measured PDFs. The solid line shows the theoretical result, Eq. (17), the dashed line, for comparison, a normal distribution with same mean and standard deviation, and the dotted line a normal distribution based on the measured sizes of the final-stage bubbles.
Power spectral density according to the individual fish chirp model, Eq. (15), and normally distributed active bubble sizes with and (solid line). A fitted power-law curve that matches the high-frequency tail of the power spectral density is indicated with the dash-dotted line. The dashed line shows for comparison the same spectrum, however, with fixed .
Measured power spectral density of a single herring chirp (solid line), recorded by Wilson et al., compared to the predicted ensemble averaged spectral power law (dashed line) resulting from the acoustic model of individual herring gas release. The dotted line indicates the estimated background of the measurements reported by these authors.
Spectrogram of a single selected sample pulse recorded at a spawning aggregation of herring (reproduced from Wahlberg and Westerberg, 2003) overlaid with the expected center frequency decay that is based on a the effective flow rate estimate from the initial and final bubble size.
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