Recently-observed physical evidence for the existence of gravitational waves, and the development of a new class of sound wave, got me thinking about the many different types of waves encountered in acoustics, the history of mechanical wave discovery and the very nature of what we mean when we talk about a ‘wave’…
A wave in a very general sense might be fairly described as any collective bulk disturbance in which the change at one position is a delayed response to the change at adjacent points. This broad definition could include all sorts of phenomena such as electromagnetism, gravity, oceanic movement, sounds, and possibly even abstractions such as ideas or emotions.
In acoustics we focus on a relatively narrow range of mechanical waves, but that is not to say this array isn’t varied and very intriguing! Below is a very brief potted historical timeline mapping some of the main physical developments in mechanical waves:
|6 BC||Pythagoras investigates the origins of musical sounds and the nature of string vibrations.|
|1500s||Vincenzo Galilei studies musical string vibrations, producing perhaps the first mathematical description of a non-linear natural phenomenon.|
|1630s-1640s||Mersenne and Galileo Galilei investigate (independently), string vibrations, pendulums and resonances.|
|1678||Hooke discovers the law that bears his name, establishing the foundation for elasticity theory.|
|1686||Newton investigates the speed of oceanic waves and of sound in air. Publishes Principia, one of the most important scientific works in human history.|
|1713||Taylor completes a dynamic solution for string vibration.|
|1744-1751||Euler and Daniel Benoulli develop the equations for vibrations in beams, and calculate the normal modes for a range of boundary conditions.|
|1747||D’Alambert derives and solves the 1-dimensional wave equation for string vibration.|
|1787||Chladni publishes experimental results on modal plate vibrations.|
|1815||Sophie Germain develops the elasticity theory for plate vibrations, winning the Paris Academy of Sciences prize (a 1kg gold medal).|
|1821||Navier formulates a general theory of elasticity in solids.|
|1828||Poisson shows that two fundamental types of wave propagate within an elastic solid, longitudinal (pressure) and transverse (shear) waves.|
|1848||Stokes expounds the elastic wave descriptions, identifying specific characteristics of each wave type.|
|1887-1888||Strutt (Lord Rayleigh) investigates surface wave propagation in solids, including the discovery of the wave type that bears his title.|
|1889-1917||Lamb develops plate vibration equations, investigates seismic tremor and pulse propagation and progresses the surface wave work developed by Rayleigh, also resulting in the surface wave class bearing his name (Rayleigh waves travelling in layers).|
|1911||Love discovers a new type of surface shear wave propagating in layered solids, explaining some seismographic anomalies.|
|1921||Timoshenko develops his beam vibration theory.|
|1924||Stoneley discovers the seismic wave bearing his name, a type of ‘leaky’ Rayleigh wave that travels along material interfaces.|
|1927||Sezawa identifies another surface wave type, which also bears his name.|
|1951||Mindlin develops his plate vibration theory.|
|1956||Biot shows that two sub-types of longitudinal wave propagate in fluid-loaded poroelastic media.|
|1968||Bleustein and Gulyaev predict the existence of a new surface wave in piezoelectrics, which becomes known as the Bleustein-Gulyaev wave.|
The physical differences in each of the main wave types are best explained by the brilliant animations at:
3D Rayleigh wave: http://web.ics.purdue.edu/~braile/edumod/waves/Rwave.htm
3D Love wave: http://web.ics.purdue.edu/~braile/edumod/waves/Lwave.htm
● P-waves (Primary waves, from seismological terminology) travel fastest, with the same particle motion as airborne sound. Biot showed that two classes of P-wave, a slower and a faster version, travel in a fluid-saturated poroelastic medium.
● S-waves (Secondary waves, arriving after the P-wave) are next in the wave race, with a velocity slightly less than P-waves, and particle motion perpendicular to the propagation.
● P-waves and S-waves form the ‘body’ or ‘bulk’ wave types that travel within the medium. Surface acoustic waves (SAWs) are combinations of longitudinal and shear wave motion, with energy ‘trapped’ near the surface.
● In R-waves (Rayleigh waves) the particle motion is anti-clockwise elliptical relative to the propagation. R-waves travel more slowly than bulk waves, but can transmit plenty of energy; in seismology R-waves are named ‘ground roll’ and convey the most destructive component of an earthquake event, arriving a considerable time after the event is detected (from faster bulk waves).
● Love waves are another surface wave with horizontally polarised particle motion.
● At material boundaries waves are partially reflected, and in certain cases wave type conversions occur.
In ultrasonics, SAWs with nanometre-scale wavelengths find applications in non-destructive testing and medicine, where they can be used to manipulate tiny structures such as cells.
The new ‘surface-reflected bulk wave’ type has been used to develop a stem cell nebulisation technique aimed initially at treating lung disease. The nebulisation process is playfully described by one of the researchers as “yelling at the liquid, breaking in into vapour”. Nebulisation using piezoelectric ultrasonics in itself is not a new idea, as both medical historians and luxury domestic appliance fans will know. But the new wave allows a much higher rate of liquid transfer to be achieved than was previously possible using conventional SAWs.
What does all this have to do with gravitational waves of course? Well, not a great deal at first glance; gravitational wavelengths range from 1000s to many trillions of metres after all. But this conversation in the IOA LinkedIn group raised an interesting point: the LIGO interferometers use lasers and optics to detect the tiniest distortions in space-time; to ensure there is no seismic interference this requires considerable vibration isolation of the equipment. Consequently some of the LIGO research team members are experts in this area.
It seems that acoustical engineering and research have promising futures at every scale of physical science!
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