thesis Going into resonance

The notion of ‘resonance’ is among the most of the two frequencies, concluding that the to realize wireless communications. But familiar ideas in science. Two pendulum amplitude of the oscillation would increase all of this, it turns out, took place before clocks in resonance synchronize themselves, linearly in time, and potentially without bound. engineers really began appreciating the role sound waves of the right frequency drive One might expect this breakthrough in of resonance in more tangible mechanical strong vibrations in a drum, and photons mechanics to have propelled the resonance systems. The gradual acceptance of tuned to atomic transitions put atoms into phenomenon into the centre of physics and resonance as a mechanical phenomenon only excited states. Particle physicists often detect engineering, and yet it didn’t. Perhaps, as Bleck- took place as dramatic failures in bridges and new particles through the appearance of Neuhaus notes, that’s because Euler himself machines made engineers painfully aware of resonances in scattering data. And we all, only considered the problem as a mathematical the inadequacy of the static analysis of forces, of course, rely on resonance in our use of curiosity lacking any practical import. Euler’s and the need to consider the surprising wireless communications. results were then ignored for well over a century, effects of interactions at similar frequencies. In 1965, in his famous Lectures on Physics, until derived again independently in the Working mostly from original sources in Richard Feynman suggested that the resonance nineteenth century by Thomas Young. Oddly, Germany, Bleck-Neuhaus readily admits that concept had become so influential that every however, Young only considered the problem in his history of the resonance concept is weighted new volume of the Physical Review would connection with the analysis of tides, and so his towards German scientists. That was interesting feature at least one resonance curve — the work was also subsequently ignored, and failed for me. My knowledge of Arnold Sommerfeld characteristic absorption peak in the spectral to have any impact on mechanics in general, — learned as a physics student in the United region around the natural internal frequency of either in physics or engineering. States, mostly from his appearance in textbooks some probed oscillatory system. And yet, the of quantum mechanics — centres on his modern familiarity of the concept obscures an The gradual relativistic improvements to the Bohr model unusual history of extremely slow recognition, acceptance of of the atom, which played an important role full appreciation taking some 300 years. As Jörn in the early or ‘old’ quantum theory. Perhaps resonance Bleck-Neuhaus of the University of Bremen this was his most important contribution. notes in a recent historical review (preprint at as a mechanical But it’s fascinating to learn that in 1902, as a https://arxiv.org/abs/1811.08353; 2018), few phenomenon only young professor at a key technology institute in scientific ideas of comparable importance have took place as a Aachen, Sommerfeld played an important role come to be appreciated so slowly. result of dramatic in pushing engineers to recognize the practical In the mid-seventeenth century, Galileo failures in bridges importance of mechanical resonance — then noted that one man pulling in the right way on and machines. largely unknown. a heavy pendulum could drive it into such large Sommerfeld did so, in part, through a motion that it could then readily lift six men dramatic experiment. In the experiment, he into the air. No doubt others had seen similar Indeed, all along, until the very late arranged for a wobbly table to support a heavy effects before; Galileo recorded it. He could nineteenth century, scientists were reluctant machine. Increasing the power supplied could offer no mathematical treatment, however, and to use the term ‘resonance’ in connection with make the machine run faster, but only to a point. came to some very incorrect conclusions about anything except acoustic phenomena, where As increasing power pushed the machine faster what happens when a periodic force drives it originated. Use of the word in other fields and faster, approaching the resonance frequency a naturally oscillatory system. In particular, — especially in mechanics and the analysis of the table, onlookers could see that the extra he concluded that the resulting motion could of vibrations in machines — always included energy only made the table vibrate more violently. never be made to deviate from natural inherent some disclaimer that the link was “only by Sommerfeld, as Bleck-Neuhaus notes, “did not frequency of the oscillating system. This view, analogy”, despite the formal equivalence of fail to say that this would mean an increase of the apparently, suited his belief that the tides could the fundamental dynamical equations. fuel bill without getting anything but the risk of not be driven by the forcing of the Moon, but Use of the concept only spread with damaging the machine and the building.” The must have some other origin. the recognition of resonance-like effects phenomenon became known as the ‘Sommerfeld Despite founding classical and celestial in general acoustic systems by Rayleigh effect.’ Only later did Sommerfeld move to the mechanics, Isaac Newton never engaged and Helmholtz in the 1860s, followed University of Munich and found his hugely directly with the issue of the driven motion by experiments of William Thomson influential school of theoretical physics. of a non-astronomical harmonic mechanical demonstrating the natural resonant behaviour One of the more surprising things in system. The first modern understanding of of LC circuits. In 1885, the German physicist science is how obvious certain principles the matter — and correction of Galileo’s error Anton Overbeck entitled a paper ‘On a can seem, once understood, when they were — awaited the development of calculus in the phenomenon with electrical oscillations anything but obvious before. This history eighteenth century, when Leonard Euler solved which is similar to resonance’. As it turns out, of resonance is another good example — the problem using a differential equation much Overbeck was the first scientist ever to record the idea is obvious now to any engineering like we would write down today. He concluded the famous resonance curve, showing the undergraduate, but it challenged the best that, in the off-resonance condition, the motion voltage excited at different frequencies, and minds in science for over three centuries. ❐ of a driven oscillatory system lacking friction the peak due to resonant interaction. or damping would exhibit two components at Not soon, Heinrich Hertz linked such Mark Buchanan different frequencies — the forced frequency resonance phenomena to the generation and the natural frequency of the driven system. of propagating electromagnetic waves, and Published online: 1 March 2019 He also considered the case of resonant match Guglielmo Marconi soon exploited them https://doi.org/10.1038/s41567-019-0458-z

Nature Physics | VOL 15 | MARCH 2019 | 203 | www.nature.com/naturephysics 203