# Sonar & Radar Simulator - Echo Ranging, Bat Echolocation, Radar Equation, Ultrasound

> Animated echo ranging and range resolution, bat Doppler, ocean sound speed and ray bending, radar equation range and PPI scope, speed radar, ultrasound depth.

- URL: https://qilingtools.com/en/physics/sonar-radar
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

It starts with a single pulse going out, hitting a target and coming back: an animation of echo ranging in air, seawater, tissue and radio that shows why range resolution is cτ/2. Then come bat FM calls and Doppler compensation, the Mackenzie sound-speed profile and ray bending in the ocean, the radar equation with a PPI scope you can click to add targets, the cosine effect in police speed radar, and medical ultrasound frequency, imaging depth and tissue-boundary reflections.

## How to use

1. In Echo ranging pick a medium, set two target distances and the pulse width, and see whether the echoes overlap
2. In Bat echolocation adjust bat and prey speeds and watch the wavefronts, echo delay and Doppler shift
3. In Ship sonar choose an ocean profile or set temperature, mixed layer and salinity to see the SOFAR channel and ray paths
4. In Radar equation & PPI set power, band, antenna size and target RCS, read the maximum range and click the scope to add targets
5. In Medical ultrasound change the probe frequency to trade resolution for depth, and inspect A-mode echoes from tissue layers

## Features

- Pulse round-trip animation with an A-scope, range resolution and maximum unambiguous range
- Bat FM and CF call spectrograms, two-way Doppler and Doppler compensation
- Mackenzie seawater sound speed, SOFAR channel axis and ray tracing in layered water
- Radar equation with antenna gain, noise power, pulse integration, SNR vs range and a PPI scope
- Speed radar Doppler shift in X, K and Ka bands with the cosine effect
- Ultrasound wavelength, axial and lateral resolution, imaging depth, impedance reflection and TGC

## FAQ

### Why is range resolution cτ/2?

A pulse has a physical length cτ. Two targets Δd apart return echoes 2Δd/c apart in time, and the echoes only stop overlapping when that gap is at least the pulse width τ, so Δd ≥ cτ/2. Finer detail needs shorter pulses (or pulse compression), which is why medical ultrasound pulses are only two or three cycles long.

### How do bats use the Doppler effect?

When a bat flies toward an insect, the insect hears a raised frequency, and the echo is raised again when the moving bat receives it, giving a two-way shift of about 2v/c. Constant-frequency bats such as horseshoe bats lower their call so the echo lands on the narrow band where their cochlea is most sensitive, and pick out prey from the tiny frequency flutter of beating wings.

### What is the SOFAR channel?

Sound in seawater speeds up with temperature and with pressure (depth). Warm surface water cools with depth, so speed falls at first; deeper down the temperature hardly changes and pressure pushes the speed back up, leaving a minimum around 600–1200 m. Rays always bend toward lower speed, so they oscillate around this layer without touching the surface or floor, and low-frequency sound can travel thousands of kilometres.

### If the radar cross section drops 10 000 times, how much range is lost?

A radar echo makes a round trip, so its power falls as 1/R⁴ and the maximum range scales with the fourth root of the RCS. Cutting the RCS to 1/10 000 only cuts the range to 1/10. That is why stealth needs RCS reductions of several orders of magnitude to matter, and why raising transmit power buys surprisingly little range.

### Why does ultrasound need gel, and why can it not see the lungs?

Reflection at a boundary depends on the impedance mismatch: R = ((Z₂−Z₁)/(Z₂+Z₁))². Air and skin differ by about 4000×, so 99.9% of the energy bounces back; the gel pushes the air out from under the probe. Lungs are full of gas and bone has a very high impedance, so sound is almost entirely reflected or absorbed and leaves a shadow behind them, which is why ultrasound is used mainly for soft tissue and fluids.

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