Page 19 - January 2009

Fig. 1. Early measurements of sound speed. Insofar as is possible, the measurements are referred to 15°C and ranges are shown where there is sufficient information to present them. Three of the ranges shown are: (N) Newton’s, (W) Walker’s, and (D) Derham’s measurements. The solid red line is at the value for the sound speed at 15°C; the dashed red line is Newton’s prediction for sound speed. The spread in published values dropped dramatically with Derham’s 1708 paper. (Values from Lenihan (1952), Walker (1698), and Derham (1708).)
observed that the sounds of cascades on the river were loud- er and clearer at night even though the tropical forest was noisier at night. Humboldt reasoned that small, turbid irreg- ularities in the atmosphere caused by solar heating of the ground during the day might scatter and attenuate sounds over relatively short distances. The British acoustician, John Tyndall, embraced Humboldt’s explanation, named the tur- bid irregularities flocculence, and interpreted many observa- tions as consequences of this flocculence.
In contrast, George Stokes had reasoned in 1857 that the normal increase in wind speed with height above the ground would bend or refract sound waves causing them to be lifted above the ears of observers upwind of the source and bent back down to observers downwind. Two decades later, Osborne Reynolds provided convincing proof of Stokes hypothesis over short ranges. At that time, Joseph Henry was head of the US Lighthouse Board and charged with evalua- tion of acoustic fog signals to supplement coastal lighthous- es. Henry believed that refraction, not flocculence, produced the wide variation in audibility of these acoustic signals.
The experiments of Derham and Henry bookend a col- lection of adventures in understanding the transmission of sound through the air. Intervening events are chronicled else- where [For example, T. Gabrielson, “Refraction of sound in the atmosphere,” Acoustics Today, 2006]; here we consider the contributions of the largely forgotten Rector of Upminster.
In 1708, Derham published what was, at the time, the seminal paper on the propagation of sound in the atmos- phere. His decision to write this paper in Latin may have resulted in wider readership across the Continent in the 1700’s, but, by the 1800’s, researchers relied largely on a small collection of translated excerpts in contemporary publica- tions. An abbreviated translation was published in the Abridged Transactions of the Royal Society in 1809 but it was not until James Welling took an interest in Henry’s experi- ments that the complete paper was translated into English.
Derham’s paper is important for several reasons. First, he addressed the question of the speed of sound in far greater depth than anyone else had. In 1697, Isaac Newton—a more senior member of the same Royal Society to which Derham belonged—published the first edition of Principia, his trea- tise on physics. In this work, Newton predicted what the speed of sound should be based on the density and static compressibility of air. Contemporary measurements of the speed of sound had sufficient variation that Newton found values both above and below his prediction; consequently, Newton was unaware how far his prediction was in error.
By 1708, however, more careful measurements suggested that Newton’s value was about 20 percent low. By far, the largest set of these measurements was assembled by Derham. Derham and others had reduced the measurement uncer- tainty sufficiently far that Newton’s prediction was no longer tenable. In subsequent editions of Principia, Newton wove several creative and ultimately unsupportable arguments as to why his values, if properly corrected, did in fact agree with measurement. [See R. S. Westfall, “Newton and the fudge fac- tor,” Science 179, 751-758, 1973. For example, Westfall writes “...[Newton’s] use of the “crassitude” of the air particles to
raise the calculated velocity by more than 10 percent was nothing short of deliberate fraud.”]
Newton should have quit while he was ahead. His calcu- lation was flawed but neither he nor anyone else of that era understood the consequences of the miniscule temperature changes experienced by air under normal acoustic compres- sion and expansion. Another century and a half would pass before the consequences of coupled temperature and pres- sure oscillations during the passage of an acoustic wave were understood clearly. [See B. S. Finn, “Laplace and the speed of sound,” Isis 55(1), 7-19, 1964.]
Derham’s extensive collection of sound speed measure- ments forced Newton’s hand; Newton’s prediction was well below the range of Derham’s measurements. (See Fig. 1.)
However Derham’s work was much more than a simple table of sound speed measurements. He investigated the effects of atmospheric conditions on the propagation of sound— both as regards speed and intensity. He established definitively that sound propagation was faster with the wind and slower against the wind.
Naturally, Derham’s work was also naïve: he dutifully recorded barometric pressure that has little effect on sound speed or propagation, and did not record temperature that does influence sound speed and propagation. At the begin- ning of the 18th century, however, these errors are under- standable—wind has a far larger effect on sound speed than temperature and it would have been difficult to arrange an experiment to isolate the smaller temperature effect; even Newton failed to emphasize the connection between temper- ature and sound speed in his theory. [Newton’s prediction for sound speed was wrong because he used the static compress- ibility of air instead of the dynamic (“adiabatic”) compress- ibility. But he still would have known that density of air is a function of temperature and that would have made his isothermal sound speed a function of ambient air tempera- ture. Had Newton suggested explicitly that there should be a dependence of sound speed on ambient temperature, the
18 Acoustics Today, January 2009