# Can we measure distance from the animal harmonic calls?

Harmonic calls have a fundamental frequency (f0) and integral multiples of that frequency as harmonic frequencies. Since the lower frequency sound wave has a low attenuation rate and the higher frequency band has high attenuation rate, is there any possibility to measure animal distance (with a single mic setup) depending on the attenuation rate of different frequency bands, now or in future?

• The question is quite broad, while the question describes a very specific method for ranging. Are you interested in single receiver ranging in general, or only in a frequency relative attenuation technique? Also, many techniques are environment specific (e.g. the ocean) so please be specific about the environment of interest. Jun 27 at 17:45

It should be possible, if frequency dependence of Source Level is known.

Take the sonar equation

RL(f) = SL(f) -20*log10(R) -at(f)*R

RL: receive level (in dB); SL: source level (in dB); R: range (m); at: attenuation dB/m;

Simplest case Source level SL(f) = SL0 = constant then range R is estimated by solving

R=(RL(f1)-RL(f2)) / (at(f1)-at(f2))

It should also be possible if the frequency dependency is known and can be factored out SL(f) = SL0 * F(f), where F(f) is the known relative frequency dependency.

You have to solve, however, the following equation

F(f2)*RL(f1)-F(f1)RL(f2) = (F(f2)-F(f(1)) * 10log10(R) + (F(f2)*at(f1)-F(f1)*at(f2)) * R

It is possible in principle given that two properties are quantified well enough: 1) (on-axis) source level 2) directionality. Both of these are kind of tricky to measure for directional sounds, and so they'd affect how accurate the distance estimate will be.

As @WMXZ pointed out, knowing the (on-axis) source level will help get the first estimate.

Sound directionality can however mess with the distance estimate a lot. Sound radiation models like the piston in an infinite baffle and others can help understand how much directionality is expected based on the size of the source and frequency.

The piston in an infinite baffle has two parameters, the wavenumber of sound (k, where k=2pi/wavelength) and the radius of the piston (a). If the product kais high then you can already see drops of upto 20 dB a few degrees off-axis. A naive omnidirectional model may then overestimate the distance of the source by a factor of 10.

There are a series of other sound radiation models (piston in a finite baffle, vibrating cap of a sphere) which may suit the needs of various sources differently (e.g. the piston in an infinite baffle results in front-back symmetry in ). I implemented some of these models in the beamshapes package, which can be used to quantify the extent to which directionality affects source range estimation.

With multi-harmonic calls, in fact you could estimate both the off-axis angle, and the source range estimation together. For an example of multi-harmonic directionality calculation check out this example here.

• thanks for the links to the beamshape package and the examples.There is the hypothesis that killer whales use the frequency dependent directionality as a cue of orientation: dx.doi.org/10.1007/s00265-002-0508-9 Jul 30 at 9:48