Connectors in Acoustical Conduits
R. Bruce Lindsay · Physical Review · 1929
Transmission through a connector.---Employing the horn theory of Webster the power transmission through an acoustical connector joining two conduits is calculated when the law of the change of area of the connector is of the form $S={S}_{0}\ensuremath{\varphi}(x)$. The general result is applied to the following special cases: 1. Conical connector, $S={S}_{0}{x}^{2}$, for which it is found that the transmission approaches unity with increasing $\mathrm{kl}$, where $l$ is the length of the connector and $k=\frac{2\ensuremath{\pi}}{\ensuremath{\lambda}}$; curves are given showing the exact dependence of the transmission on frequency for various values of $l$ and the expansion ratio $m$. 2. Bessel connectors of higher order, $S={S}_{0}{x}^{a}$ where $a$ can take all values, in which case it is found that the transmission for $\mathrm{kl}$ large approaches a value approximately independent of $a$. 3. Exponential connector, $S={S}_{0}{e}^{\mathrm{ax}}$, the limiting case of the Bessel connectors, with a transmission ratio showing little difference from that of the former. 4. The connector whose generating curve has a point of inflection, $S={S}_{0}{e}^{\ensuremath{-}a{x}^{2}}$, for which for large $\mathrm{kl}$, the transmission differs little from that of the previously discussed connectors. These theoretical results are in agreement with certain transmission experiments of G. W. Stewart.Phase change due to a connector.---The phase change introduced by the connector is calculated for the special cases mentioned and is shown to approximate $\mathrm{kl}$ in the limit of increasing $\mathrm{kl}$.