Problem — Ultrasound wavelength in an ultrasound scan

Problem

An ultrasound scan uses ultrasound at $f = 2\;\text{MHz}$. In soft tissue the speed of sound is about $1500\;\text{m/s}$. What is the wavelength? Comment on why this value determines the minimum resolution of the image.

Solution

Wavelength. $v = \lambda f$, with $f = 2\cdot 10^{6}\;\text{Hz}$:

$\lambda = \frac{v}{f} = \frac{1500}{2\cdot 10^{6}} = 7{,}5\cdot 10^{-4}\;\mathrm{m}$

$\ev{\lambda \approx 0{,}75\;\mathrm{mm}}$

Comment on resolution. Because of diffraction, a wave cannot “see” details much smaller than its own wavelength: two structures closer together than $\sim\lambda$ are not distinguished. With $\lambda \approx 0{,}75$ mm the resolution is sub-millimetre. To resolve finer details, higher frequencies are used (smaller λ), at the cost of lower penetration into tissue.

Collegamenti

Argomenti: Waves Concetti: Period and frequency · Diffraction