# If I don't know the source level of an animal's vocalization, is there still a meaningful way to measure how loud the signal is?

I am working with a remote species, and as far as I am aware there is no data on source levels or an audiogram available.

We placed the single recorder within a breeding area and have, at multiple times, observed only this single species within the recorder's range. Additionally, we have photographs with associated photogrammetry data (laser rangefinder) of the species within the recorder's range.

With this information, can we figure out the average loudness of a species' vocalization?

• Two questions for clarification - (1) is it just a single recorder or can you localize? (2) in your title for the question do you mean source level when you say "loud" or "loudness" or do you mean received level or something else? Jun 22 at 14:19
• Matthews et al. 2016 would be helpful here, if you did have multiple hydrophones doi.org/10.1121/1.4978299 Jun 22 at 14:22
• @selene i meant to imply one recorder, hence 'placed the recorder' but I can clear that up. :) Also, maybe I misunderstood but I was trying to use more 'common' language here. To write as someone that didn't know the recieved level equation. That term is not obvious to all outside of our field. Which is why Doug's answer below is great because he explains it. Jun 23 at 6:01
• Also see related question and answers here bioacoustics.stackexchange.com/q/3/131 Jun 23 at 9:13

## 1 Answer

If your hydrophone system is calibrated, then it sounds like you do have the information you need to estimate a source level using a simple sonar equation: RL = SL-TL (Received level = Source Level - Transmission Loss). Your problem is going to be how to estimate TL as a function of range. In open water, this would be close to 20log10(range), but in a shallow environment, it may be quite different. I'd advise making the RL measurements and plotting them against range, then trying a range of TL values such as 10log(r), 15log(r), 20log(r) and see what the spread is of SL values. If you can get your hands on a sound source that can produce sounds at a similar frequency, you might also be able to directly measure TL in that environment. Key to studies like this though is accepting that you're unlikely to get a perfect answer, so understanding and reporting the uncertainty on your measurements is almost as important as the measures themselves.

• Having a calibrated microphone is the key here. Calibration means that you know what voltage level (or digital level) you will get out of a microphone for a specific physical sound level (dB SPL) at a specific frequency. Jun 22 at 13:57
• The question is not specific to underwater acoustic as far as I understand, so maybe you could take this into account in your response to make it more general (e.g. avoid "hydrophone", "open water")? Or mention that you are answering for underwater acoustics only?
– Noil
Jun 22 at 15:03
• You're right. My bad. The same basic idea applies though in air just as in water. Jun 22 at 20:28
• Thank you Doug! Perhaps we can add the terrestrial equation, too? Jun 23 at 6:06
• I'm a water guy. In air, the basic physics are the same, but I'll defer to those who work in air to give additional advice on things to watch out for when making these measurements, e.g. the effects of wind, attenuation, etc. Jun 25 at 13:25