Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/427

the wave on the ends of the enclosure is equal to the mean pressure increase throughout the enclosure.

The proof of the proposition rests in showing that the velocity of sound can be correctly calculated by the assumption of the proposition as hypothesis.

Thus the compression wave will be in equilibrium when its rate of communication of momentum to the ends of the enclosure is equal to the added pressure.

Momentum of wave	$=m\ U.$
Momentum communicated by each reflexion	$=2\ m\ U.$
Number of reflexions per second	$={\frac {U}{2\ l}}$
∴ force due to momentum of wave	$={\frac {m\ U^{2}}{l}}$	(1)

Let $P_{1}$ be the mean pressure exerted by the additional mass $m$ distributed throughout the enclosure; then, by Boyle's law, ${\frac {P_{1}}{\rho }}=k,$ where $k$ is a constant,

and	$\rho \ {\frac {m}{l}}$
or	$P_{1}={\frac {m\ k}{l}}$	(2)
by (1) and (2)	${\frac {m\ U^{2}}{l}}={\frac {m\ k}{l}}$
or	$U^{2}=k$
∴	$U={\sqrt {k}}={\sqrt {\frac {P}{\rho }}}$

which is the well-known result; by substituting for $P$ and $\rho$ (abs. units) for air at any stated temperature the Boyle's law velocity is obtained; this is, of course, subject to Laplace's correction for the actual velocity.

The above reasoning, though here given as a disproof of Larmor's theorem as a generalisation, is in reality a valid and simple method of determining the velocity of sound. If we cast aside the mythology introduced into the subject by the light radiation specialists, and treat the question as it should be

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