Answer to Question #88452 in Molecular Physics | Thermodynamics for gc

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

Answer 1

To find the size of the smallest feature observable in human tissue using ultrasound we calculate the ultrasound wavelength λ using the formula

$$\lambda =\frac{c}{f}$$

where c is the speed of sound in human tissue, f is the frequency of sound. We are given

$$c=1,540\text{ }m/s=1.54\cdot {{10}^{3}}m/s, \\ f=15\,\,MHz=1.5\cdot {{10}^{7}}Hz \\$$

Substituting these values in the formula, we get

$$\lambda =\frac{c}{f}=\frac{1.54\cdot {{10}^{3}}m/s}{1.5\cdot {{10}^{7}}Hz}\approx 1.03\cdot {{10}^{-4}}m$$

Since one meter equals 100 centimeters we get

$$\lambda \approx 1.03\cdot {{10}^{-4}}\,m\cdot 100\,cm/m=1.03\cdot {{10}^{-2}}\,cm$$

We can also write the wavelength in millimeters

$$\lambda \approx 1.03\cdot {{10}^{-2}}\,cm\cdot 10\,mm/cm=1.03\cdot {{10}^{-1}}\,mm \\ =0.103\,mm \\$$

So the size of the smallest feature observable in human tissue when examined with 15-MHz ultrasound is 0.103 mm