Simulator — try the sonar equation

What the screen shows

• Sound speed c — from the Mackenzie approximation
• Wavelength λ — c / f
• Absorption coefficient α — a teaching-grade frequency-dependent approximation
• One-way TL — spreading + absorption
• Round-trip time — 2R / c
• DI — the idealized 10 log10(N)
• Passive / active SNR — estimated from the simplified equations

Real ocean acoustics is far more complex, but for an introduction, seeing the first-order terms at work on a single screen is enough.

The absorption coefficient α (educational simplified formula)

This simulator and the minimal implementation in Chapter 7 compute the absorption coefficient α [dB/km] from frequency f [kHz] using the following educational simplified formula:

α [dB/km] = 0.11 · f² / (1 + f²)
          + 44   · f² / (4100 + f²)
          + 0.000275 · f²
          + 0.003

This formula simplifies the form of the François-Garrison (1982) and Ainslie-McColm (1998) full models by dropping the temperature, salinity, pH, and depth dependence and keeping only the frequency dependence. Each term corresponds to a physical process:

• Term 1, 0.11 f² / (1 + f²): absorption from boric acid (B(OH)₃) relaxation, dominant at low frequencies (below about 1 kHz).
• Term 2, 44 f² / (4100 + f²): absorption from magnesium sulfate (MgSO₄) relaxation, dominant in the mid-frequency band (up to a few tens of kHz).
• Term 3, 0.000275 f²: absorption from the viscosity of pure water, dominant at high frequencies (above a few hundred kHz).
• Term 4, 0.003: a constant floor term that keeps the calculation numerically well behaved (educational use).

This formula is an approximation of typical seawater (around 10 °C, 35 PSU, and 100 m depth). For real-world design, use the full François-Garrison or Ainslie-McColm models including temperature, salinity, pH, and depth as inputs.

Preset parameter details

The specific values applied by each preset button are:

For example, the High freq. · strong attenuation preset uses 120 kHz over 800 m, where absorption dominates and drives the active SNR down to about −33 dB. Predict the dominant terms from these numbers before moving the sliders, and the simulator becomes easier to read.

SO101 sonar simulator

Simulator settings are saved only in this browser's localStorage. This is a simplified teaching model — for real-world design you will need refraction, boundary scattering, reverberation, and a full absorption model.

Four things to watch first

1. Increase range — TL grows and SNR falls.
2. Raise frequency — wavelength shrinks, but absorption rises too.
3. Add elements — DI grows and the system gains against noise.
4. Active — the extra 2TL makes things harsh at long range, quickly.

Takeaways from this chapter

• Move range, frequency, and element count, and the dominant term in TL and SNR becomes clear.
• High frequencies give short wavelengths but suffer more absorption.
• Active gets hard fast at long range because of the 2TL penalty.