Euler: From Sound to Light 155
On the other hand, Euler ’ s arguments brought forward other aspects of waves that are
no less consequential and cannot be taken for granted. He took the pulse theory as it had
developed in the work of Descartes and Huygens but changed it by adding a new element
of periodicity , so that Casper Hakfoort cautions us to call it a “ periodic pulse theory ” rather
than simply a “ wave theory. ”^8 This leads to the most innovative part of Euler ’ s theory,
which connected this periodicity to the phenomenon of color. In this development, already
his earliest auditors remarked that “ what is special in the hypothesis of Mr. Euler is its
parallel between sound and light. ”^9 Euler specifically applied this analogy to extend the
propagation of pulses from sound to light. Beginning with his 1727 calculation of the
speed of sound (in his youthful “ Dissertation on Sound ” ), Euler now applied a similar
argument to light, considered as pulses in a “ subtle ” ether that has a finite, if small, density
and hence a finite velocity of propagation, as opposed to Descartes ’ s and Huygens ’ s
instantaneously propagating medium. By comparing the ratio of known sound and light
velocities with his calculations about the strength of materials, Euler arrived at very nearly
the same ratio of the ether ’ s elasticity to its density from both calculations, which he took
as further confirmation of his fundamental analogy and its physical preconditions.
From there, Euler constructed propagating light pulses, which are not yet fully waves
but still very close to sound pulses, each considered as a sequence of traveling zones of
higher state of motion, whether in air or in ether ( figure 10.2 ). Defining the distance
between pulses as d , their frequency f , and velocity of propagation v , Euler gives their
fundamental relation d = v/f , which is the basis for his account of color. Note that he does
not speak of “ wavelength ” — for indeed these are not waves but traveling pulses — but of
the frequency of the pulses. Not a whole “ wave ” but the individual pulses are primary for
him; Euler considers that the pulses can be “ isochronic, ” equally spaced pulses correspond-
ing to a single musical pitch of frequency f , or “ nonisochronic ” pulses having no single
spacing d and hence no single frequency.Figure 10.2
Euler ’ s diagram of the propagation of a sequence of pulses, from his “ New Theory of Light ” (1746).