Intermediate Physics for Medicine and Biology: The Rayl

Section 13.3 of Intermediate Physics for Medicine and Biology discusses acoustic impedance. For an ultrasonic wave the acoustic impedance is the pressure divided by the tissue velocity, so it has units of Pa/(m/s). In terms of kilograms, meters, and seconds, the units of acoustic impedance are kg/(m² s).

Acoustic impedance is analogous to electrical impedance. Voltage over current is like pressure over velocity. Electromagnetic waves propagating through a transmission line reflect when the electrical impedance changes, just as ultrasonic waves propagating through tissue reflect when the acoustic impedance changes. The unit for electrical impedance is the ohm, and the unit for acoustic impedance is the…

Wait! What is the name of the unit for acoustic impedance? According to IPMB the units of acoustic impedance are kg/(m² s). It has no name. The newton is a kg m/s², the joule is a kg m²/s², the pascal is a kg/(m s²), and the watt is a kg m²/s³. Why is there no name for the kg/(m² s)?

There is a name. A kg/(m² s) is called a rayl. It’s pronounced “rail.” I quote the last lines of Section 13.3.1 in IPMB, but using the rayl.

The quantity Z = ρ₀c = √ρ₀ κ is called the acoustic impedance of the medium [ρ₀is the density, c is the speed of sound, and κ is the compressibility]. The acoustic impedance of water is about (10³ kg m^-3)(1400 m s^-1) = 1.4 × 10⁶ rayl, or 1.4 Mrayl. The acoustic impedance of air is about 400 rayl, so Z_air is much less than Z_water (Denny 1993).

The rayl is also the name for a g/(cm² s). But the rayl in the meter-kilogram-second system of units isn’t the same as the rayl in the centimeter-gram-second system. A CGS rayl is equal to ten MKS rayls. Maybe all this confusion is why no one uses the rayl (including IPMB). My vote is to abolish the CGS rayl. Erase it from history. Make it taboo. Let’s restrict the use of the term rayl to the MKS rayl.

Theory of Sound, by Lord Rayleigh, superimposed on Intermediate Physics for Medicine and Biology.

The Theory of Sound,
by Lord Rayleigh.

The unit is named after John William Strutt, better known as Lord Rayleigh (pronounced ray-lee). He is known for Rayleigh waves, Rayleigh scattering, Rayleigh-Benard convection, the Rayleigh criterion, the Rayleigh-Taylor instability, the Rayleigh-Ritz method, and the Rayleigh-Jeans law. His influential textbook The Theory of Sound makes him the logical choice for the unit of acoustic impedance. He won the Nobel Prize in 1904 “for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies.”

Below are excerpts from Rayleigh’s Nobel biography.

John William Strutt, third Baron Rayleigh, was born on November 12, 1842 at Langford Grove, Maldon, Essex…

Throughout his infancy and youth he was of frail physique; his education was repeatedly interrupted by ill-health, and his prospects of attaining maturity appeared precarious. After a short spell at Eton at the age of 10, mainly spent in the school sanatorium, three years in a private school at Wimbledon, and another short stay at Harrow, he finally spent four years with the Rev. George Townsend Warner (1857) who took pupils at Torquay.

In 1861 he entered Trinity College, Cambridge, where he commenced reading mathematics, not at first equal in attainments to the best of his contemporaries, but his exceptional abilities soon enabled him to overtake his competitors. He graduated in the Mathematical Tripos in 1865 as Senior Wrangler and Smith’s Prizeman. In 1866 he obtained a fellowship at Trinity which he held until 1871, the year of his marriage.

A severe attack of rheumatic fever in 1872 made him spend the winter in Egypt and Greece. Shortly after his return his father died (1873) and he succeeded to the barony, taking up residence in the family seat, Terling Place, at Witham, Essex… In 1876 he left the entire management of the land to his younger brother.

From then on, he could devote his full time to science again. In 1879 he was appointed to follow James Clerk Maxwell as Professor of Experimental Physics and Head of the Cavendish Laboratory at Cambridge. In 1884 he left Cambridge to continue his experimental work at his country seat at Terling, Essex, and from 1887 to 1905 he was Professor of Natural Philosophy in the Royal Institution of Great Britain, being successor of Tyndall…

Lord Rayleigh’s first researches were mainly mathematical, concerning optics and vibrating systems, but his later work ranged over almost the whole field of physics, covering sound, wave theory, colour vision, electrodynamics, electromagnetism, light scattering, flow of liquids, hydrodynamics, density of gases, viscosity, capillarity, elasticity, and photography… His Theory of Sound was published in two volumes during 1877-1878, and his other extensive studies are reported in his Scientific Papers – six volumes issued during 1889-1920…

He had a fine sense of literary style; every paper he wrote, even on the most abstruse subject, is a model of clearness and simplicity of diction. The 446 papers reprinted in his collected works clearly show his capacity for understanding everything just a little more deeply than anyone else…

Lord Rayleigh… was a Fellow of the Royal Society (1873) and served as Secretary from 1885 to 1896, and as President from 1905 to 1908. He was an original recipient of the Order of Merit (1902), and in 1905 he was made a Privy Councillor. He was awarded the Copley, Royal, and Rumford Medals of the Royal Society, and the Nobel Prize for 1904…

Lord Rayleigh died on June 30, 1919, at Witham, Essex.

Rayleigh has always been a hero of mine. The breadth of his contributions, the quality of his writing, the ability to excel at both theory and experiment, and the service he contributed to his profession amaze me. I’m glad Russ Hobbie and I discuss some of his contributions in Intermediate Physics for Medicine and Biology.