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Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition by Tim Mellow, Leo Beranek

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9.11. Infinite exponential 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 e m x
image (9.39)
where S T is the area of the throat, which is located at x   =   0. In the steady state, the Helmholtz equation for the exponential horn is obtained by inserting S(x) from Eq. (9.39) into Eq. (2.27) to yield
( 2 x 2 + m x + k 2 ) p ˜ ( x ) = 0
image (9.40)
where
k = 2 π

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