Bird songs and frog calls obey the same physics as any acoustic wave: their intensity falls with distance, their high frequencies are absorbed by humid air, and they refract upward or downward depending on the temperature profile of the atmosphere. Understanding this physics is necessary for interpreting passive acoustic monitoring data — an apparent decline in calling activity could reflect a real change in calling behaviour or simply a shift in propagation conditions.

Module 04

Acoustic Physics in Ecological Contexts

Sound Propagation in Natural Environments

Sound propagation in real environments departs from free-field assumptions due to geometric spreading, atmospheric absorption, vegetation scattering, and ground effects.

Geometric Spreading (Spherical) \[ I(r) = \frac{P}{4\pi r^2} \quad \Longrightarrow \quad L(r) = L_0 - 20\log_{10}(r/r_0) \] Doubling distance reduces intensity by 6 dB in free field. In a sound duct (cylindrical spreading), only 3 dB per doubling — the physical origin of the dawn chorus amplification.

Atmospheric Absorption \[ \alpha(f, T, h) = \frac{f^2}{\rho c}\left[\frac{\eta_{\rm vis}}{3} + \frac{(\gamma-1)^2 \kappa}{c_p} + \sum_i \frac{A_i f_{r,i}}{f_{r,i}^2 + f^2}\right] \] Viscous + thermal + molecular relaxation losses. High-frequency calls (>8 kHz) suffer dramatically more attenuation — a key driver of evolution toward lower frequencies for long-distance communication.

Vegetation Scattering \[ \Delta L_{\rm veg}(f) \approx a \cdot f^{0.4} \quad \text{dB/100 m} \] $a$ is habitat-specific (0.5–2 for temperate deciduous forests). Sub-linear frequency dependence — low-f signals travel farther through vegetation. Explains why many forest birds converge on 1–4 kHz.

The Acoustic Window Hypothesis

Every habitat has a characteristic acoustic window — a frequency range of minimum attenuation. Species evolve calls that fit within this window.

Habitat	Acoustic Window	Mechanism
Closed-canopy rainforest	1–2 kHz	Vegetation filters high-f; ground absorption filters low-f
Open grassland	4–8 kHz	Wind turbulence dominates low-f
Aquatic (shallow)	0.2–2 kHz	Surface reflection creates constructive interference
Urban environment	>3 kHz	Traffic noise dominates <1 kHz; urban birds shift accordingly

Implications for monitoring

Because attenuation depends on frequency, temperature, humidity, and vegetation cover, "detected species richness" in PAM (Module 6) must be corrected for propagation. Statistical methods (distance sampling, occupancy modelling) absorb propagation effects into observation models.

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