Sound in seawater travels roughly 4.4x faster than in air (~1500 m/s), spreading spherically from the source while losing energy to geometric spreading and molecular absorption — the two terms of sonar transmission loss.
TL = 20·log10(r) + α(f)·r/1000 (spherical spreading + absorption, dB)
RL = SL − TL (received level)
λ = c / f, c ≈ 1500 m/s (wavelength)
t = r / c (travel time)
- Source level — the loudness of the call/sonar ping at 1 m from the source (dB re 1 µPa).
- Frequency — pitch of the emitted sound; lower frequencies (like blue whale calls) carry further with less absorption.
- Receiver distance — how far the listening point (or a listening whale) sits from the source.
- Water absorption — scales the frequency-dependent absorption coefficient, mimicking salinity/temperature/depth effects.
Real marine mammals exploit exactly this physics: low-frequency whale calls travel ocean-basin distances via the deep sound channel, while dolphins use high-frequency echolocation clicks for short-range, high-resolution prey detection.