Passive ultrasound sonar

Kragen Javier Sitaker, 2016-12-28 (1 minute)

Up to a quarter megahertz, ultrasound attenuates in air at about 20dB/ft/MHz, which is 66dB/m/MHz. The Airy limit is sin θ = 1.220λ/D for a circular aperture. Mach 1 is 331 m/s.

Could you do passive ultrasound sonar at a reasonable resolution? At 100kHz you have 6.6dB/m of attenuation, so you only have about 20 meters of range where a detectable amount of sound is going to reach you. λ = 3.3 mm, so the Airy limit for a 100mm aperture is 0.040 radians, about 2.3 degrees. You’d need a much larger aperture to get close to the theoretical far-field limit of what 100kHz could resolve.

At a higher frequency, like 1MHz, you only have a couple of meters of range, so you’d have to get super lucky to have an ultrasound source in range. 1MHz in air has a 330-micron wavelength, so your limit would be 4.2 milliradians, about a quarter of a degree, and then you really could see stuff with subcentimeter resolution at a meter of distance or so. But in practice you probably need an active ultrasound source for that.

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