Explore with the Simulator

First, see what changes when you change one input

Before following each equation, try these four changes. Keep the other inputs fixed and move only one control at a time so the cause and effect stay clear.

1. Increase range: one-way transmission loss (TL) and round-trip time increase, while signal-to-noise ratio (SNR) falls.
2. Raise frequency: wavelength becomes shorter, but absorption tends to increase, making long-range propagation harder.
3. Add elements: directivity index (DI) increases, making it easier to recover the signal from noise.
4. Use active sonar: sound travels to the target and back, so the SNR equation contains 2TL. Range therefore has a larger effect than it does in passive sonar.

Start by switching among the presets to compare the overall patterns. Then change one slider at a time.

What the screen shows

• Sound speed c: calculated from temperature, salinity, and depth with the Mackenzie approximation.
• Wavelength λ: calculated with λ = c / f.
• Absorption coefficient α: a teaching formula estimates how strongly sound is absorbed at the selected frequency.
• One-way transmission loss (TL): the sum of spreading loss and absorption loss.
• Round-trip time: the time for the transmitted sound to reach the target and return, calculated with 2R / c.
• Directivity index (DI): an idealized array-gain estimate using 10 log10(N).
• Passive and active SNR: estimates based on the simplified equations used earlier in the course.

The real ocean also introduces reflections, refraction, reverberation, and other effects. This simulator keeps the focus on the main relationships.

Compare the four presets

Each preset applies all of the values shown below. Predict the result from the table before clicking a preset; this makes it easier to identify which input drives the result.

For example, High frequency · high absorption sends a 120 kHz signal over 800 m and back. Absorption is large, and active SNR falls to about −33 dB.

SO101 sonar simulator

Settings are stored only in this browser's localStorage and are not sent to a server. This is a simplified teaching model. Real-world design also needs refraction, surface and seafloor scattering, reverberation, and a more complete absorption model.

A simple way to work through the simulator

1. Select Shallow · short range and use its values as your baseline.
2. Change only range and watch one-way TL, round-trip time, and both SNR values.
3. Restore the range, then change only frequency and compare wavelength with absorption.
4. Finally, change element count and confirm that DI and SNR move by the same amount.

Supplement: the absorption formula used by the simulator

This section explains the formula in more detail. To use the simulator, it is enough to remember that absorption tends to increase as frequency rises.

The simulator and the implementation in Chapter 7 calculate absorption coefficient α [dB/km] from frequency f [kHz] with this simplified teaching formula:

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

This is a learning-oriented simplification of the François-Garrison (1982) and Ainslie-McColm (1998) models. It removes their dependence on temperature, salinity, pH, and depth. The terms roughly represent:

• 0.11 f² / (1 + f²): low-frequency absorption from boric acid (B(OH)₃) relaxation.
• 44 f² / (4100 + f²): mid-frequency absorption from magnesium sulfate (MgSO₄) relaxation.
• 0.000275 f²: high-frequency absorption caused by the viscosity of pure water.
• 0.003: a constant term used in this teaching formula.

This formula gives a rough estimate for typical seawater. Real-world design should use a complete model that includes temperature, salinity, pH, and depth.

Takeaways from this chapter

• As range increases, transmission loss and round-trip time increase, while SNR falls.
• As frequency increases, wavelength becomes shorter, but absorption tends to grow.
• Adding elements increases DI and helps improve SNR.
• Active sonar pays the round-trip 2TL penalty, so range has a larger effect.