Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

9.10. Infinite conical horn

Theoretical considerations

The equation describing the cross-sectional area S(x) as a function of the distance x along the axis is

S ( x ) = S T ( x / x T ) 2

(9.32)

where S _T is the area of the throat, which is located at a distance x   =   x _T ahead of the apex at x   =   0. In the steady state, the Helmholtz equation for the conical horn is obtained by inserting S(x) from Eq. (9.32) into Eq. (2.27) to yield

( ∂ 2 ∂ x 2 + 2 x ∂ ∂ x + k 2 ) p ˜ ( x ) = 0

(9.33)

where

k = 2 π λ = ω c

(9.34)

and