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Acoustic radiation force is a physical phenomenon resulting from the interaction of an acoustic wave with an obstacle placed along its path. Generally, the force exerted on the obstacle is evaluated by integrating the acoustic radiation pressure (due to the presence of the sonic wave) over its time-varying surface.

The magnitude of the force exerted by an acoustic plane wave at any given location can be calculated as:[1][2]

$${\displaystyle |F|={\frac {2\alpha I}{c}}}$$

where

• F is the force in kg/(s2cm2),
• α is the absorption coefficient in Np/cm,
• I is the temporal average intensity of the acoustic wave at the given location in W/cm2, and
• c is the speed of sound in the medium in cm/s.

The effect of frequency on acoustic radiation force is taken into account via intensity (higher pressures are more difficult to attain at higher frequencies) and absorption (higher frequencies have a higher absorption rate). As a reference water has an acoustic absorption of 0.002 dB/(MHz2cm).[3]

Acoustic radiation forces on compressible particles such as bubbles are also known as Bjerknes forces, and are generated through a different mechanism, which does not require sound absorption or reflection.[4]
References

Palmeri, Mark; Sharma, Amy; Bouchard, Richard; Nightingale, Roger; Nightingale, Kathryn (October 2005). "A finite-element method model of soft tissue response to impulsive acoustic radiation force". IEEE Trans Ultrason Ferroelectr Freq Control. 52 (10): 1699–712. doi:10.1109/tuffc.2005.1561624. PMC 2818996. PMID 16382621.
McAleavey, S. A.; Nightingale, K. R.; Trahey, G. E. (June 2003). "Estimates of echo correlation and measurement bias in acoustic radiation force impulse imaging". IEEE Trans Ultrason Ferroelectr Freq Control. 50 (6): 631–41. doi:10.1109/tuffc.2003.1209550. PMID 12839175. S2CID 12815598.
Diagnostic ultrasound imaging : inside out. ISBN 9780126801453.
Leighton, T.G., Walton, A.J. and Pickworth, M.J.W., 1990. Primary bjerknes forces. European Journal of Physics, 11(1), p.47.

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