What are the fundamental limitations of echolocation in Earth's atmosphere?

I'm writing a cyberpunk novel where one of the characters has an augmentation that allows them to echolocate.

The idea is that there is a device on the center of his forehead (is there a more optimal location?) that produces extremely low-wavelength wavelets of sound at a very high rate. The wavelets are ultrasonic, so he has to have some kind of ear-implant that transfers the information to his brain. Since human brains aren't adapted to processing sound with such extreme precision, he also has to have a brain implant that assists with the necessary computations.

My question is about how powerful this ability could get, assuming there are no restrictions on how fast the implants work.

According to wikipedia, bats can echolocate with a frequency >200 kHz. Let's assume a frequency of 200 kHz. $\lambda = \frac{343 \;m/s}{200,000 \;Hz} = 1.7 \;mm$ is the wavelength of the sound, right? Does that mean that anything wider than 1.7 millimeters could hypothetically be detected? Obviously, this can't be true at large enough distances, so I don't think I'm approaching the problem correctly.

What is the upper bound on the frequency that could be used? What is the relationship between resolution and distance? How do both of these things change if the echolocator is moving at high speeds?

posted over 5 years ago

Eben Cowley‭

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