Abstract
Sound plays two important roles in medicine and biology: animals hear sound and thereby sense what is happening in their environment, and physicians use high-frequency sound waves called ultrasound to image structures inside the body. We first derive the wave equation governing the propagation of sound, and then discuss the many properties of waves including frequency, wavelength, the speed of sound, the acoustic impedance, the intensity, and attenuation measured by the decibel scale. We review the anatomy of the ear and describe how hearing occurs. We then analyze how physicians use ultrasound imaging for medical diagnosis, including piezoelectric transducers, pulse echo techniques, and Doppler imaging.
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Notes
- 1.
We might be looking at a wave whose properties depend on all three coordinates, \(x\), \(y\), and \(Z\), but where, in the region we are studying, the dependence on \(y\) and \(Z\) is very slight. This is like the 1-D electrostatic approximations in Chap. 6.
- 2.
See Sect. 1.12; we ignore any forces arising from viscosity, gravity, or surface tension.
- 3.
Strictly speaking, the acoustic impedance is the ratio \(Z=p_{0}/v_{0}\), and carries information about both the amplitude ratio and the relative phase of the pressure and velocity. If the waves are in phase, \(Z\) is said to be resistive; if they are \(\uppi /2\) out of phase, \(Z\) is said to be reactive. The characteristic acoustic impedance is a property of the medium: \(Z_{0}=\rho _{0}c\). Both have units Pa m s\(^{-1}\) or kg m\(^{-2}\,\)s\(^{-1}\). For a plane wave, the impedance is resistive and \(Z=Z_{0}.\) For other waves, such as standing waves, there is a reactive component.
- 4.
ICRU 61 (1998).
- 5.
Sometimes the attenuation coefficient is expressed in nepers m\(^{-1}\), in which case the natural logarithm of the intensity or pressure ratio is used.
- 6.
- 7.
We use \(d\xi /dt\) because it is in phase with the excess pressure.
- 8.
Litho- means stone.
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Hobbie, R., Roth, B. (2015). Sound and Ultrasound. In: Intermediate Physics for Medicine and Biology. Springer, Cham. https://doi.org/10.1007/978-3-319-12682-1_13
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DOI: https://doi.org/10.1007/978-3-319-12682-1_13
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