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Chapter 0 Approx. 4–5 hours 36 questions total Graded in-browser Saved locally

Understand Underwater Acoustic Sonar with Diagrams and Exercises

An introductory course that covers why sound is used underwater — speed of sound, round-trip time, passive vs. active, transmission loss, SNR, and array gain — through diagrams, short exercises, and an in-browser simulator.

Overall0 / 360%
StoragelocalStorage onlyNothing is sent to a server
FormatDiagrams + exercises + simulator + implementationNo external libraries
Start with Chapter 1 Try the simulator first Resume where you left off
1 Introduction — what sonar does

Why sound is the natural tool underwater, and the first distinction between passive and active.

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2 Speed, wavelength, and range — the acoustic ruler

Line up the four-piece set of speed of sound, wavelength, and round-trip time.

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3 Passive vs. active — two sensing modes

Sort out how the passive and active equations differ, and where TS and 2TL enter.

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4 Transmission loss and SNR — the reach equation

Read TL, noise, and array gain as simple addition and subtraction in dB.

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5 Arrays and beamforming — pointing a virtual ear

Get a feel for arrays, delay-and-sum, and the ideal array gain.

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6 Simulator — try the sonar equation

Drag sliders for frequency, range, and number of elements.

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7 Implementation and review — writing sonar calculations in vanilla JavaScript

Close with a minimal implementation in vanilla JavaScript and a mixed review.

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Diagram → hand calculation → simulator → implementation

As in the other courses in this series, we proceed in the order build intuition with a diagram → work short exercises by hand → check with an in-browser simulator → read a minimal implementation. We do not jump straight into advanced propagation models; the goal is first to read which term dominates using a first-order approximation.

Approx. 4–5 hours36 questions totalGraded in-browserSaved in localStorageNo external libraries

The six equations we keep reusing

distance = c × t / 2Convert the echo round-trip time into one-way range (active)
λ = c / fGet the wavelength from speed of sound and frequency
TL ≈ N log10(R) + αR[km]A rough approximation of spreading plus absorption
SNRpassive = SL - TL - (NL - DI)The simplified passive sonar equation
SNRactive = SL - 2TL + TS - (NL - DI)The simplified active sonar equation
DI ≈ 10 log10(N)A minimum approximation of the ideal array gain

The point of this course is not to memorize these, but to learn in which situation which term dominates.

Chapter overview

ChapterContent
Chapter 1 / 5 questionsIntroduction — what sonar does. Draw the first line between passive and active.
Chapter 2 / 5 questionsSpeed, wavelength, and round-trip time. Get the minimum set for range and resolution.
Chapter 3 / 5 questionsPassive vs. active sonar. Keep target radiated sound and echo conceptually separate.
Chapter 4 / 5 questionsTransmission loss and SNR. Read reach as addition and subtraction in dB.
Chapter 5 / 5 questionsArrays and beamforming. Get the first feel of delay-and-sum and the directivity index.
Chapter 6 / 4 questionsSimulator. Play with the trade-off between range, frequency, and element count.
Chapter 7 / 7 questionsImplementation and review. Tie equations and code together in vanilla JavaScript.

Tips for studying

  1. Read the body text and then solve the exercise right below. Reading alone makes it hard to retain the feel of dB and round-trip time.
  2. Through Chapter 4, write one line of the equation on paper. That makes it much harder to overlook the 2TL factor.
  3. In the Chapter 6 simulator, move range only, frequency only, and element count only — one at a time.
  4. In Chapter 7, line up each equation with its function name as you read. That anchors the material.

Prerequisites

  • High-school level logarithms, exponents, and unit conversion are enough.
  • This course uses simplified introductory models. Rigorous ocean acoustic propagation and reverberation are out of scope.
  • We target ocean measurement, fisheries survey, and passive monitoring use cases, and do not go into tactical operational detail.
  • Everything runs on static HTML / CSS / JavaScript alone, with no external libraries.

A short primer on dB (decibels)

Throughout this course, sound pressure levels, transmission loss, and SNR are all expressed in dB (decibels). The decibel is a logarithmic unit for ratios, defined as L [dB] = 10 log₁₀(P / P₀) for power ratios. The advantage is that multiplications turn into additions in dB, so transmission loss, array gain, and noise reduction can all be combined by simple arithmetic.

  • +3 dB ≈ ×2 (power) / +10 dB = ×10 / +20 dB = ×100
  • −3 dB ≈ ÷2 / −10 dB = ÷10 / −20 dB = ÷100
  • Spherical spreading 20 log₁₀(R) means a 10× increase in range adds 20 dB of loss.

Underwater acoustics deals with quantities (sound pressures, losses) that span many orders of magnitude, and the dB scale makes graphs and equations much easier to read.

Goal of this course

  • Explain in words why sound is the natural choice underwater.
  • Use distance = c × t / 2 and λ = c / f by hand.
  • Explain the difference between the passive and active equations, especially the meaning of 2TL and TS.
  • Have a feel for the ideal array gain 10 log10(N).
  • Read a minimal implementation in vanilla JavaScript and match equations to code.

A caveat about this course

The simulator and equations in this course are educational first-order approximations. In real ocean settings, sound-speed-profile refraction, boundary reflection, sea-floor / sea-surface scattering, reverberation, bandwidth, detection thresholds, and sensor characteristics all matter. Please use the SNR values here as a way to grasp "direction and dominant terms" rather than as absolute predictions.

Public references consulted

Go to Chapter 1 →