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I have a relatively specific thought on acoustic masking, and wanted to know what others think, or if folks know of studies that have addressed this problem.

When studying acoustic masking, we often think about the frequency range of a signal of interest, say for example high frequency whistles of odontocetes, and then examine the overlap of a competing signal that might be causing masking, say for example boat noise. In scenarios where there is strong overlap between the two signals, for example, the whistle at 5 kHz and the boat noise in the 10 Hz to 10 kHz range, and the noise source has higher amplitude than the signal of interest, we would say that there is a high level of acoustic masking.

However, now imagine a scenario where the noise source is in a different frequency range. For example, the odontocete whistle is at 15 kHz, but the noise source is in the 10 Hz to 10 kHz range. If we viewed the two signals on a spectrogram, both sources would be clearly visible. Definitions of masking that I'm aware of would suggest that masking is not occurring. However, what if the noise source had sufficiently high amplitude such that it was still difficult for the receiver to hear the whistle? At some high amplitude, a temporary threshold shift would occur, along with effectively "clipping" of the receiver's hearing system. But how well can animals hear around high amplitude sounds, effectively using a bandwidth filter to only focus on the signals of interest while ignoring adjacent high amplitude sounds? Is there some quantifiable cutoff below the level for hearing damage?

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You ask about masking and hearing damage due to masking.

Both happens at the receiver.

So, when you say: "both sources would be clearly visible", then masking would not have occured.

Now, sure, off-band masking can occur:

If you replace the FFT based spectrogram (STFT) by an auditory based filter bank (e.g. Mel-scale), then you will note that not only the frequencies are spaced (nearly) logarithmically but the spectral width is very wide.

This widening of the spectral band width results in picking up energy from the masking band, whereby sound at lower frequencies is masking at lower enery levels than masking sound above the band of interest. You will see this in the mel-scale spectrogram.

This effect will happen also with FFT based spectrograms, as each FFT has a spectral response function that, dending on the selected analaysis window will have spectral side lobes (spectral leakage). For a rectangular window (FFT without windowing function) any off band noise > (signal +40 dB) will mask the signal of interest.

Bandpass filter around the frequencies of interest will always inprove the situation, especially signals that are far away from the frequency band of interest. (e.g. removing 50/60 Hz from audio)

However, as animals (including homo) process audio in the brain, they can generate spectral filter that narrow to the frequency of interest and reducing the effect of masking.

Further (especially in homo), there is the cognitive part of audio processing, where you hear what your Natural NN (Brain) predicts that you will hear next.

Now, concerning Noise Induced Hearing Loss (NIHL), I first quote https://www.nidcd.nih.gov/health/noise-induced-hearing-loss which says

When you are exposed to loud noise over a long period of time, you may slowly start to lose your hearing. Because the damage from noise exposure is usually gradual, you might not notice it, or you might ignore the signs of hearing loss until they become more pronounced. Over time, sounds may become distorted or muffled, and you might find it difficult to understand other people when they talk or have to turn up the volume on the television.

This quote clearly indicates that NIHL is the result of all possible scenarios, so the question: "Is there some quantifiable cutoff below the level for hearing damage?"(emphasis mine) is extremely difficult to answer, and a lot of research is going on to determine NIHL, but it seems that there is NO easy quantifiable safe masking level.

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great question! I don't know the answer, but searching for "auditory masking" might get you the information you're looking for. Auditory masking research seeks to understand perception rather than just frequency-time overlap.

A quick google scholar search for 'auditory masking in animals' turned up research on:

marine mammals (https://link.springer.com/article/10.1007/s10071-022-01671-z)

and frogs (https://www.sciencedirect.com/science/article/pii/S0003347207003314?casa_token=7SIYEe6dpaIAAAAA:4KigNMgzmYEEGLWXW6xAb86Cq3YKpFTkUQNquRJqEm7SPCNjH1Ndtc_pOLTUN8_3QFfYgXwg4j4)

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