Time Reversal is a signal processing technique that can be used to focus wave energy to a selected point in space. It started in the 1960s as a technique for signal transmission in the ocean between ships. It has been used for underwater acoustic communications, biomedical lithotripsy using focused ultrasound, earthquake localization and characterization, detecting and imaging cracks and defects in structures (nondestructive evaluation), and focusing sound in rooms. At BYU, Brian Anderson and his students have extended the use of time reversal for nondestructive evaluation and have been exploring the use of time reversal to produce focused sound in rooms.
B. E. Anderson, M. Griffa, C. Larmat, T. J. Ulrich, and P. A. Johnson, “Time reversal,” Acoust. Today 4(1), 5-16 (2008). //dx.doi.org/10.1121/1.2961165
B. E. Anderson, M. C. Remillieux, P.-Y. Le Bas, and T. J. Ulrich, “Time reversal techniques,” Chapter 14 in Nonlinear Acoustic Techniques for Nondestructive Evaluation, 1st Edition, Editor Tribikram Kundu, ISBN: 978-3-319-94476-0 (Springer and Acoustical Society of America), pp. 547-581 (2018). //dx.doi.org/10.1007/978-3-319-94476-0
Explanation of Time Reversal Focusing
Below is a video that illustrates the time reversal process from a single source to a single receiver location. An impulse is broadcast from the source on the left and an impulse response is obtained by a receiver on the right. The impulse response is reversed in time and broadcast by a source located at the original receiver location on the right. The waves retrace their original paths but with a timing such that they arrive at the original source location on the left simultaneously.
Below is another video animation of the time reversal process but this time with the use of four sources. During the forward step each source sequentially broadcasts a pulse and the impulse response is obtained from each source to the "focal location" (denoted by the black dot) independently. The impulse responses are reversed in time and then broadcast simultaneously during the backward step of the time reversal process. Circular waves are broadcast for each emission in an impulse response and these waves scatter around the room. A portion of these waves that are broadcast arrive simultaneously at the focal location to provide the constructive interference that can be used to generate high amplitude time reversal focusing.
LEGO Demonstration of Time Reversal Focusing
In order to demonstrate the power of time reversal focusing we have conducted some fun experiments to knock over selected LEGO minifigures using focused vibrations. Vibrations are generated in a plate using speaker shakers that are designed to play music through your desk or table top. An impulse response between each shaker and a target location is obtained and then these impulse responses are reversed in time and played simultaneously from the shaker(s) (sometimes we only use one!). Waves then constructively interfere at the target location, focusing energy momentarily at that location. We can then knock over a LEGO minifigure at that location without knocking over other nearby minifigures. Check out the video below showing experimental data that shows waves being focused and then some fun demos of LEGO minifigures being knocked over. BYU produced a nice video of the demonstration as well. This demonstration will be featured in a Wave Propagation Museum exhibit at ETH Zurich hopefully starting in the summer 2021.
More information about this demonstration can be found in two papers we wrote:
C. Heaton, B. E. Anderson, and S. M. Young, “Time reversal focusing of elastic waves in plates for educational demonstration purposes,” J. Acoust. Soc. Am. 141(2), 1084-1092 (2017). https://dx.doi.org/10.1121/1.4976070
L. A. Barnes, B. E. Anderson, P.-Y. Le Bas, A. D. Kingsley, A. C. Brown, and H. R. Thomsen, “The physics of knocking over LEGO minifigures with time reversal focused vibrations,” J. Acoust. Soc. Am. 151(2), 738-751 (2022). https://doi.org/10.1121/10.0009364