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Chapter 0 Approx. 3–4 hours 36 questions total Graded in-browser Saved locally

Underwater Acoustics and Sonar: A Visual, Hands-On Course

Learn why sound is used underwater, how sonar measures range and finds signals in noise, and how an array narrows down the direction of arrival. The course combines diagrams, 36 exercises, an in-browser simulator, and a JavaScript implementation.

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 — Why Sound Works Underwater

Learn why sound is useful for underwater sensing, then meet passive and active sonar and the basic range equation.

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2 Sound Speed, Wavelength, and Travel Time — The Basics of Range

Relate sound speed, wavelength, and frequency, then calculate one-way range from round-trip travel time.

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3 Passive and Active Sonar — Listening versus Measuring Echoes

Compare listening to sound from a source with transmitting a sound and measuring its echo.

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4 Transmission Loss and SNR — Can the Signal Arrive and Be Detected?

Estimate transmission loss, then combine source, noise, directivity, and target strength to calculate SNR.

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5 Arrays and Beamforming — Focusing on a Direction

See how multiple hydrophones are combined and how element count, beam width, and grating lobes are related.

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6 Explore with the Simulator

Change one condition at a time and observe how transmission loss and SNR respond.

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7 Implement the Equations in JavaScript and Review

Implement the equations in plain JavaScript, then reconnect the ideas through practical examples.

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What You Will Learn

Light is easily affected by turbidity and scattering underwater, while radio waves do not travel well over long distances. Sound therefore plays a central role when we need to examine a wide underwater area. Sonar uses travel time, the strength of returning sound, and differences in arrival time across multiple receivers to estimate range, direction, bottom topography, and whether a target is present.

This course focuses on the foundations shared by ocean observation, bathymetry, fisheries surveys, and environmental monitoring. Instead of starting with a complex theory, we build understanding in four steps: calculate range, detect an echo, distinguish a signal from noise, and focus on the direction from which the sound arrives.

Six Equations Used throughout the Course

distance = c × t / 2Use the echo's round-trip travel time t to calculate one-way range.
λ = c / fAt the same sound speed c, a higher frequency f gives a shorter wavelength.
TL ≈ K log₁₀(R) + αR[km]Use spreading coefficient K and absorption coefficient α to estimate geometric spreading and absorption loss.
SNRpassive = SL - TL - (NL - DI)Check whether sound radiated by the source can be distinguished from ambient noise.
SNRactive = SL - 2TL + TS - (NL - DI)Account for loss on both the outgoing and returning paths of an active-sonar echo.
DI ≈ 10 log₁₀(N)Under idealized assumptions, more receiving elements N make it easier to suppress noise from other directions.

You do not need to memorize the equations. The goal is to explain which quantity changes in each situation and why.

Tips for Studying

  1. After reading a section, solve the exercise directly below it. Round-trip time and dB become much clearer after one calculation.
  2. Through Chapter 4, write the equation on one line before substituting numbers. This makes the 2TL term in active sonar harder to miss.
  3. In Chapter 6, change only one condition at a time: range, frequency, or element count.
  4. In Chapter 7, place each equation beside its JavaScript function and follow the calculation from input to output.

Prerequisites

  • High-school-level logarithms, exponents, and unit conversion are enough.
  • We do not derive fluid mechanics or signal-processing theory in depth. The priority is to put conditions into an equation and interpret the result.
  • JavaScript powers the in-browser grading and progress storage, but no programming experience is needed until Chapter 7.

A Short Primer on dB (Decibels)

This course expresses sound levels, losses, and signal-to-noise ratio (SNR) in dB (decibels). Convert a power ratio with 10 log₁₀(P / P₀) and a sound-pressure ratio with 20 log₁₀(p / p₀). In the sonar equations used here, the levels are already expressed in dB and can be added or subtracted directly.

  • For power ratios, +3 dB ≈ ×2, +10 dB = ×10, and +20 dB = ×100.
  • For sound-pressure ratios, +6 dB ≈ ×2 and +20 dB = ×10.
  • Spherical spreading 20 log₁₀(R) means that increasing range by a factor of 10 adds 20 dB of loss.

Sound levels and losses span a wide range in underwater acoustics. The dB scale makes those changes easier to compare in equations and graphs.

Course Goals

  • Explain in your own words why sound is used for underwater sensing.
  • Calculate range and wavelength with distance = c × t / 2 and λ = c / f.
  • Explain the difference between passive and active sonar, especially the meanings of 2TL and target strength (TS).
  • Explain how the idealized directivity-index approximation DI ≈ 10 log₁₀(N) relates to element count.
  • Match JavaScript functions to their equations and follow the calculation from input to output.

About the Approximations in This Course

The equations and simulator are first-order teaching approximations. In the real ocean, results are also affected by refraction from the sound-speed profile, reflection and scattering at the surface and bottom, reverberation, bandwidth, detection thresholds, and sensor-specific characteristics. Treat the displayed SNR as a way to understand the direction of change and the most influential terms, not as an absolute prediction.

References

Go to Chapter 1 →