Ultrasound probes can resolve structural details with sizes approximately equal to the wavelength

Question

Ultrasound probes can resolve structural details with sizes approximately equal to the wavelength of the ultrasound waves themselves. What is the size of the smallest feature observable in human tissue when examined with 17-MHz

 ultrasound? The speed of sound in human tissue is 1,540 m/s.

Answer 1

If you are asking "what is the wavelength of a 17-mhz wave traveling 1540 m/s?" Then the answer would be found with the following formula for sinusoidal waves.

λ = ν / ƒ

where,

λ = wavelength [m]

v = speed of the waveform [m/s]

ƒ = frequency of the waveform [Hz]

*you can verify the above formula with dimensional analysis [m/s] / [Hz] = m/s * s = m (the unit of wavelength)

For this specific calculation, we are trying to find λ. v would be 1540 m/s and ƒ would be 17 * 1,000,000 hz (1 MHz = 1,000,000 Hz). plug all this in.

λ = 1540 / 17,000,000 ≈ .000088 m which is roughly 1/10th of a millimeter, almost small enough to make out the brain of a presidential nominee.

Of course this is only a theoretical rough estimate under the ideal conditions and assumptions made using this formula i.e being in a linear medium with constant wave speed. I hope this helped answer your question.