Fig 1.
Reverberation generated by humpback whale song units.
(a) Amplitude measures of units from a humpback whale song recorded off the coast of Maui in 2007 with a high signal-to-noise ratio (~48 dB), give the misimpression that little is happening acoustically during the intervals between units. (b) A spectrographic representation (FFT = 2048; Hann window; 95% overlap) that emphasizes frequency contours and harmonics of units, such as is commonly used to classify song phrases, shows reverberation as hazy bands between units that may appear similar to background noise and that are much less salient than units. (c) Reducing the frequency range and adjusting the brightness and contrast settings of the spectrogram shown in (b) reveals prominent bands of reverberation (highlighted with arrows) that persist long after each unit is produced. (d) a spectral analysis (FFT = 4096; Hann window; 50% overlap) of the interval of “silence” following the second unit in this example shows that the peak frequency of narrowband reverberant energy generated by the first unit (centered near 360 Hz) is ~40 dB above ambient noise levels more than 3 s after the unit has ended. Additionally, this spectrum shows that a reverberant “tail” generated by the second unit (centered near 130 Hz) falls just below a tail generated by the first unit (180 Hz; ratio = 1.3), with no spectral overlap.
Fig 2.
Reverberation generated by drone units.
A subset of units (vertical bands) generated at regular intervals, produces a narrow band of reverberant acoustic energy (horizontal band centered at 165 Hz) that persists until just before the unit is repeated; these drone units typically occurred in multiple different sound patterns within a song. Note that the two units following the drone unit in the 3-unit pattern shown here also reverberate, but across a broader range of frequencies and less consistently. (2007 Maui recording; FFT = 8192, Hann, 50% overlap).
Table 1.
Acoustic properties of drone units.
Mean (standard deviation) measures of frequency with peak energy (Peak), unit duration (Dur) and period of drone unit repetition (Period) for all recordings.
Fig 3.
Variability of drone units across repetitions.
(a) Spectrogram (FFT = 4096, Hann window, 50% overlap) of 210 consecutive drone units (with following units/silences removed) recorded near Réunion Island shows that the frequency content of these units remained highly stable throughout the 26 min recording. (b) Spectrogram of 132 consecutive drone units recorded off the coast of Puerto Rico shows subtle shifts in the spectral content of these units over time, with energy consistently focused near 130 and 500 Hz.
Fig 4.
Variability of drone units across repetitions.
(a) Spectrogram (FFT = 17200, Hann window, 50% overlap) of 251 consecutive drone units (sans following units/silences) recorded near Colombia shows gradual shifts in spectral content with repetition, as well as more discrete shifts in spectral content. (b) Spectrogram (FFT = 8192, Hann window, 50% overlap) of 163 drone units recorded off the coast of Maui in 2002 shows a large shift in fundamental frequency. (c) A similar shift in drone unit frequency content was evident in the Madagascar recording (57 units).
Fig 5.
Examples of all repeated sound patterns sung by a humpback whale near Réunion Island.
(left) Spectrograms show variations in the number and features of units following drone units (FFT = 4096; y-axis = 0–1.4 kHz). Arrows show how frequencies with peak energy content straddle a reverberant band that matches the fundamental frequency of the drone units. (right) Spectra (FFT = 8192) calculated across all instances of drone units (dotted gray lines) and all following units (black lines) for each pattern type show that the distribution of spectral energy within following units spans regions surrounding frequencies with peak energy from drone units (vertical dashed lines); note, in particular the areas between the two spectra curves.
Fig 6.
Examples of all repeated sound patterns sung off the coast of Puerto Rico.
(left) Spectrograms show variations in the number and features of units following drone units (FFT = 4096; y-axis = 0–1.4 kHz). Dashed lines show how frequencies with peak energy in drone units are systematically related to, and even interdigitated with, the peak frequencies of following units. (right) Spectra (FFT = 8192) calculated across all instances of drone units (dotted gray lines) and all following units (black lines) for each pattern type show that the distribution of spectral energy within following units spans regions adjacent to frequencies with peak energy from drone units (vertical dashed lines); note, in particular the areas between the two spectra curves. Arrows show peak frequencies of following units that are adjacent to peak frequencies of drone units.
Fig 7.
Examples of all repeated sound patterns sung off the coast of Maui (2007).
(left) Spectrograms (FFT = 4096; y-axis = 0–1.4 kHz) show variations in the number and features of units following drone units (1st, 2nd, 4th, and 5th images), as well as when drone units were not part of a pattern (3rd row). (right) Spectra (FFT = 8192) calculated across all instances of drone units (dotted gray lines) and all following units (black lines) for each pattern type show that the distribution of spectral energy within following units spans regions adjacent to frequencies with peak energy from drone units. Arrows show peak frequencies of following units that are adjacent to peak frequencies of drone units. For the sound pattern without drone units, the spectrum of the longest duration unit in the pattern was used as a basis for comparison.
Fig 8.
Examples of spectral interleaving involving alternating units.
(a) Spectrogram (FFT = 8600; y-axis = 0–1.4 kHz) of a Colombian song shows repeated alternations of a drone unit and following unit. (b) Spectra (FFT = 17200) calculated across all instances of drone units (dotted gray line) within the pattern shown in (a), and all following units (black lines), show that the spectral peaks of following units (381 and 387 Hz) border those of drone units (281 Hz; ratio = 1.4); the thinner solid line is the spectrum of the last three units. (c) Spectrogram (FFT = 4096; y-axis = 0–1.4 kHz) from the Maui 2002 recording shows similarly alternating units. (d) Spectra (FFT = 8192) calculated across all instances of drone units (dotted gray line and solid gray line) within the pattern shown in (c) and all following units (black lines) show that the spectral peaks of following units (161 and 291 Hz) span regions adjacent to those of drone units (peaks of 140 and 522 Hz); the thinner lines are spectra of the last three units (gray = 1st and 2nd, black = 3rd). (e) Spectrogram of a second complex pattern from the Maui 2002 recording showing mixing of drone units with following units. (f) Spectra of drone (156 Hz peak) and following units (178 Hz peak; ratio = 1.1) show tight spectral interleaving within the pattern. x-axis time/frequency scales apply to all spectrograms/spectra other than (f).
Table 2.
Relationships between frequencies with peak energy across sequences of units.
Maxima of spectra for lower (Peak 1) and higher (Peak 2) frequency peaks measured from all units within different pattern types (Figs 5–7). Spectra from all drone units used within a pattern type were compared with spectra from associated following units. Ratios were calculated by dividing the higher frequency of a pair by the lower frequency.