It might be said that radiation pressure is a phenomenon that the observer thinks he understands—for short intervals, and only every now and then.
R. T. Beyer [1]
Radiation force refers to the time-averaged force exerted by waves on objects they encounter. "Time-averaged" refers to integration of a periodic function over a cycle and division by the corresponding period. "Waves" can refer to waves on a string, surface waves in water, acoustic waves, and electromagnetic waves, for example.
The incident wave fields can be traveling, standing, or any combination of the two, but radiation forces are generated only by propagating waves (as opposed to evanescent waves), the reason for which will be explained later in these notes. The taxonomy of waves is displayed below:
For real-world examples of radiation force, see:
For not-so-real (but very illustrative) examples of radiation force, see:
I had originally attempted to reproduce Rayleigh's study of radiation forces in "simpler" oscillatory systems, namely the pendulum and string constrained by a ring, which he discussed in the papers
Philos. Mag. 3, 338-346 (1902)But the setup of these problems (especially the role that the ring plays, and the forces it experiences) makes them not so simple. For example, in the 1902 paper, I do not understand why the ring experiences an upward force \(W(1-\cos\theta)\), where \(W\) is the weight of the bob, and where \(\theta\) is the angle measured from the downward direction. Since Rayleigh's examples seem rather contrived (both in their setup and the manner in which they are solved), and since I did not find them particularly relevant to the study of acoustic, electromagnetic, etc. radiation forces, I am currently working on a simpler example that makes sense to me: the radiation force exerted by a transverse traveling wave on a string on a bead free to move on the string.
Philos. Mag. 10, 364-374 (1905).
These notes may contain typos—please contact me if you find any.
These notes were inspired by a lunch discussion with Profs. G. W. Swift, R. Waxler, L. Zhang, A. A. Atchley, J. Mobley, J. D. Maynard, and M. F. Hamilton at the 2024 Physical Acoustics Summer School (PASS). I am grateful to Prof. L. A. Ostrovsky for our email discussions about acoustic radiation force. Thanks to Prof. P. S. Wilson for the "acoustic fountain" demo. Also, thanks to Dr. R. P. Williams for helping me think through Rayleigh's pendulum [Philos. Mag. 3, 338-346 (1902)], and to Mr. J. S. Hallveld for his contributions to the discussion on whether acoustic radiation force should be regarded as a linear or nonlinear effect.