Rotating Horn Simulation

Horn source-position model:

$$\underline{x}_s(t) = \left[\begin{array}{c} r_s\cos(\omega_m t) \\ [2pt] r_s\sin(\omega_m t) \end{array}\right] \protect$$

where

$$\begin{eqnarray*} r_s &=& \mbox{circular radius}\\ \omega_m &=& \mbox{angular velocity} \end{eqnarray*}$$

This expression ignores any directionality of the horn radiation, and approximates the horn as an omnidirectional radiator located at the same radius for all frequencies.

Horn source-velocity model:

$$\underline{v}_s(t) \;=\;\frac{d}{dt}\underline{x}_s(t) \;=\;\lef... ...in(\omega_m t) \\ [2pt] r_s\omega_m\cos(\omega_m t) \end{array}\right] \protect$$

For circular motion about the origin, tangential velocity is always orthogonal to the position