A diagnostic ultrasound scanner can be operated at 2.0 MHz or at 8.0 MHz

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Acoustics of fluids: generation, propagation and attenuation · Acoustics of fluids: generation, propagation and attenuation

Fluids and Continuum Physics, Ch Acoustics: sound propagation, radiation and attenuation

Problem

A diagnostic ultrasound scanner can be operated at 2.0 MHz or at 8.0 MHz. To estimate how the two settings differ in penetration, model the tissue as water and use the classical absorption coefficient, which accounts for viscosity alone,

\alpha = 2\omega^{2}\mu/(3\rho_0 c^{3})

, with the amplitude of a plane wave falling as

e^{-\alpha x}

. For water take

\mu = 1.0\times10^{-3}

Pa s,

\rho_0 = 1000

kg m

^{-3}

and

c = 1483

m s

^{-1}

. ((a)) Estimate

\alpha

at 2.0 MHz. ((b)) By what factor is

\alpha

larger at 8.0 MHz than at 2.0 MHz? ((c)) Estimate the distance over which the amplitude falls to

1/e

of its starting value at 8.0 MHz.

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