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Är knappast något matte geni men om jag uppfattat följande text korrekt kan ekvationen ovan beskriva hur horn och ljudledningshögtalare till viss del är relaterade. Lite slarvigt utifrån ekvationen kan ljudledningshögtalare anses vara omvända horn trots de är helt väsensskilda. Begreppet används av bla David Griesinger. (https://www.helpnetsecurity.com/2016/03 ... ity-shape)
Båda delar i praktiken (ej i det ideala fallet), fast på olika sätt, problem med resonanser.
Tumregler enligt Martin King:
- Resonanser måste dämpas när ljudledningshögtalaren utnyttjar fler oktaver än 3.
- Horn har problem med resonanser när förhållandet mellan hals/munarean är mindre än 1/300 för ffa högre frekvenser.
A one dimensional wave equation, as shown above, can be used to describe the
air motion in both transmission line and horn geometries. The second term on the left
side of the equals sign accounts for the flare geometry in the equation of motion. If m is
equal to zero the geometry is straight, if m is not zero the geometry is contracting or
expanding along the length depending on the sign. The third term on the left of the
equals sign accounts for distributed fiber damping in the air volume as defined by "lambda" a
viscous damping coefficient. This equation of motion is a combined result that can be
used to mathematically describe a fiber filled transmission line or an empty horn.
Restating the equation by setting the frequency dependent damping term "lambda" to zero
leaves the classic exponential horn wave equation found in most acoustics texts.
Solving the equation of motion requires the application of two boundary
conditions. At the driver end, a unit oscillating velocity is typically assumed as one
boundary condition. At the open end, the acoustic impedance of a circular piston
mounted on an infinite baffle is usually assumed as the second boundary condition. The
open end boundary condition is a source of frequency dependent mass loading
(imaginary part) and (real part).
Almost all back loaded horn designs found on the Internet are really acting as
transmission lines at low frequencies and never approach horn behavior because the
mouth is too small.
Transmission Line and Back Loaded Horn Physics
By Martin J. King, 3/29/13
http://www.quarter-wave.com/Horns/TL_an ... hysics.pdf
http://www.quarter-wave.com/
http://www.t-linespeakers.org/design/MJ ... index.html
JM