Exponential funnel

Exponential funnel on a gas pressure signal fanfare

An exponential funnel is a termination of a waveguide or a sound source that radiates like an antenna , the cross-sectional area of which is described by an exponential function :

{\ displaystyle \ A (x) = A_ {h} \ cdot e ^ {kx}}

${\ displaystyle A_ {h}}$ is the surface cross-section of the funnel neck, the funnel constant or the opening dimension of the funnel and its surface cross-section at a distance from the funnel neck. ${\ displaystyle k}$ ${\ displaystyle A (x)}$ ${\ displaystyle x}$

Technical background

At the end of a smoothly ending waveguide or sound-conducting pipe, there is a sudden change in the wave impedance, which can also be measured . Due to the resulting mismatch, most of the vibration energy is reflected back into the pipe . This leads to an ineffective emission of the sound. A waveguide that ends abruptly or a sound-conducting pipe is a bad antenna or a bad sound emitter. If, on the other hand, the end of the waveguide / sound conductor is shaped as an exponential funnel , there is a smooth transition of the wave impedance from the high value in the pipe to the lower value in the free space outside. Ideally, the reflection is very low and most of the energy is radiated.

Applications

Acoustics : The funnels of fanfares, trumpets , tubas , trombones , vuvuzelas , but also gramophones and horn speakers are ideally shaped as exponential funnels . Since the energy is radiated more effectively, they are on the one hand louder - on the other hand, wind instruments shaped in this way are also more difficult to blow cleanly due to the lower reflections and the associated lower quality of the acoustic resonances that arise; With such instruments, a compromise must always be found between volume and playability.

High frequency technology : Antennas are often implemented as exponential funnels for very high frequencies (GHz range, microwaves ). These often close off a waveguide ( horn antenna , supply of parabolic mirrors ). The single-wire waveguide is also terminated on both sides with exponential funnels, which, however, are approximated here by means of wires or rods. Another example is the Vivaldi antenna , which consists of a two-dimensional exponential horn.

literature

Stefan Weinzierl (Ed.): Handbook of audio technology. Springer Verlag, Berlin / Heidelberg 2008, ISBN 978-3-540-34300-4 .
K. Heidermanns: Electroacoustics. BG Teubner Verlag, Stuttgart 1979, ISBN 978-3-519-00080-8 .
Eberhard Zwicker, Manfred Zollner: Electroacoustics. 2nd edition, Springer Verlag, Berlin / Heidelberg 1987, ISBN 978-3-540-18236-8 .
NA Wagner, NA Aigner, NA Hahnemann, NA Hecht, Schottky, Salinger, Rüdenberg, Esau, Rukop, Möller: The scientific foundations of radio reception. Published by Julius Springer, Berlin 1927.
Reinhard Lerch, Gerhard Sessler, Dietrich Wolf: Technical acoustics. Basics and applications, Springer Verlag, Berlin / Heidelberg 2009, ISBN 978-3-540-23430-2 .
Klaus Fellbaum: Speech processing and speech transmission. Springer Verlag, Berlin / Heidelberg 1984, ISBN 978-3-540-13306-3 .

Individual evidence

↑ Hans-Herbert Klinger: Loudspeakers and loudspeaker housings for HiFi , Franzis-Verlag, Munich 1976, p. 51f, ISBN 3-7723-1058-3 .

Web links

Generation, propagation, measurement and evaluation of sound (accessed on September 1, 2017)
MODELING THE SOUND CONDUCTION OF CAR HORNS (accessed on September 1, 2017)
Horn loudspeaker: The technology behind it (accessed on September 1, 2017)

[1] Hans-Herbert Klinger: Loudspeakers and loudspeaker housings for HiFi , Franzis-Verlag, Munich 1976, p. 51f, ISBN 3-7723-1058-3 .