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Ro808
diyAudio Member

Join Date: Mar 2010
A very concise definition is:

"The “end correction” is the distance from the open end of a pipe to the antinode just above it".
This applies to standing waves in a pipe.

From Wiki:
A theoretical basis for computation of the end correction is the radiation acoustic impedance of a circular piston. This impedance represents the ratio of acoustic pressure at the piston, divided by the flow rate induced by it. The air speed is typically assumed to be uniform across the tube end. This is a good approximation, but not exactly true in reality, since air viscosity reduces the flow rate in the boundary layer very close to the tube surface. Thus, air column inside the tube is loaded by the external fluid due to sound energy radiation. This requires an additional length to be added to the regular length for calculating the natural frequency of the pipe system.

The concept of End Correction is widely used in Structural and Fluid Dynamics, Antenna Theory and notably the Acoustics of musical instruments (pipe and horn).

The point of reflection for air pressure fronts in brass instruments is not at the end of the tube, but some distance outside of it. End correction is the difference between the end of the physical tube and the actual point of reflection. This distance differs according to frequency.

There is no scientifically proven and accepted value for the end correction of a resonant tube, various values ranging from 0.3r to 0.6r have been suggested from numerous disparate experiments. Lord Rayleigh was the first scientist to publish a figure, in 1871: it was 0.3r.

Consider a pipe closed at one end and open at the other. A simple model tells that resonance will occur when the pipe length (plus end correction) is 1/4,3/4,5/4 etc. of the sound wavelength by assumption that antinode occurs at the open end. Due to the pipe wall waves can't expand freely, so there is not a perfect antinode. By addition of an end correction, the pipe appears to be acoustically somewhat longer than its physical length.

The most accurate value appears to be 0.58r (It is independent of the wavelength but does depend on the shape of the tube. Value is quoted for a circular cross section). Normally in such experiments, you eliminate (and can calculate) the end correction by finding two consecutive resonating lengths L1 and L2 at the same frequency, for example two cases where the L1+c is 1/4 wavelength and L2+c is 3/4 wavelength. Subtracting gives L2 - L1 = half wavelength. In most experiments, the speed of sound in the tube is calculated. However, it must be remembered this is not the same as the speed in free air.

Martin J. King discussed end correction in his articles on Transmission Line and Back Loaded Horn Physics.

If I'm not mistaken, Danley Soundlabs has implemented (a form of) end correction in some of their Synergy horns.
The Equivalent Throat system is one of the few theories that includes end correction in the combined application of a compression driver + horn.

The science behind the end correction is thoroughly adressed by Neville H. Fletcher and Thomas D. Rossing in "The Physics of Musical Instruments".

The topic is also discussed in the works of:
Beranek
Howard and Craig
Kurze and Riedel
Junger and Feit
Morse and Feshbach, Morse and Ingard
and numerous others.
Attached Images
 resonance_07.jpg (13.6 KB, 1521 views) End Correction.png (168.2 KB, 1522 views) End+correction+Effective+length+of+pipe+is+L+? (1).jpg (75.7 KB, 1508 views) more+radiation+should+escape+when+the+end+flares+and+less+is+reflected+(though+ripple+is+not+goo.jpg (49.9 KB, 1494 views) 1-s2.0-S0022460X09005495-gr18.jpg (183.2 KB, 1298 views)

Last edited by Ro808; 16th December 2017 at 11:57 AM.

 19th July 2018, 01:14 AM #14872 mikey_audiogeek   diyAudio Member   Join Date: Sep 2004 Location: Northland, New Zealand Bump...
 19th July 2018, 01:49 AM #14873 AllenB   diyAudio Member   Join Date: Oct 2008 I take exception to the word correction. For example, a LeCleach horn has no end, it is infinite. A conical horn cannot be ended so it cannot be corrected. Other horns have complications that make the concept of correction illogical.
 19th July 2018, 04:46 PM #14874 Retsel   diyAudio Member   Join Date: Jan 2005 Location: Ann Arbor, Michigan "I take exception to the word correction. For example, a LeCleach horn has no end, it is infinite. A conical horn cannot be ended so it cannot be corrected. Other horns have complications that make the concept of correction illogical." Why can't a roundover be added to the mouth of a conical horn to reduce resonances? Wouldn't the effect be the same as the roundover used with the LeCleach horn? Retsel
 19th July 2018, 05:03 PM #14875 gedlee   diyAudio Member     Join Date: Dec 2004 Location: Novi, Michigan A properly flared horn/waveguide will not have any significant "end correction". The concept is ill-applied to a good waveguide. __________________ Earl Geddes Gedlee Website
ivicai
diyAudio Member

Join Date: Sep 2009
Quote:
 Originally Posted by Ro808 A very concise definition is: "The “end correction” is the distance from the open end of a pipe to the antinode just above it". This applies to standing waves in a pipe. From Wiki: A theoretical basis for computation of the end correction is the radiation acoustic impedance of a circular piston. This impedance represents the ratio of acoustic pressure at the piston, divided by the flow rate induced by it. The air speed is typically assumed to be uniform across the tube end. This is a good approximation, but not exactly true in reality, since air viscosity reduces the flow rate in the boundary layer very close to the tube surface. Thus, air column inside the tube is loaded by the external fluid due to sound energy radiation. This requires an additional length to be added to the regular length for calculating the natural frequency of the pipe system. The concept of End Correction is widely used in Structural and Fluid Dynamics, Antenna Theory and notably the Acoustics of musical instruments (pipe and horn). The point of reflection for air pressure fronts in brass instruments is not at the end of the tube, but some distance outside of it. End correction is the difference between the end of the physical tube and the actual point of reflection. This distance differs according to frequency. There is no scientifically proven and accepted value for the end correction of a resonant tube, various values ranging from 0.3r to 0.6r have been suggested from numerous disparate experiments. Lord Rayleigh was the first scientist to publish a figure, in 1871: it was 0.3r. Consider a pipe closed at one end and open at the other. A simple model tells that resonance will occur when the pipe length (plus end correction) is 1/4,3/4,5/4 etc. of the sound wavelength by assumption that antinode occurs at the open end. Due to the pipe wall waves can't expand freely, so there is not a perfect antinode. By addition of an end correction, the pipe appears to be acoustically somewhat longer than its physical length. The most accurate value appears to be 0.58r (It is independent of the wavelength but does depend on the shape of the tube. Value is quoted for a circular cross section). Normally in such experiments, you eliminate (and can calculate) the end correction by finding two consecutive resonating lengths L1 and L2 at the same frequency, for example two cases where the L1+c is 1/4 wavelength and L2+c is 3/4 wavelength. Subtracting gives L2 - L1 = half wavelength. In most experiments, the speed of sound in the tube is calculated. However, it must be remembered this is not the same as the speed in free air. Martin J. King discussed end correction in his articles on Transmission Line and Back Loaded Horn Physics. If I'm not mistaken, Danley Soundlabs has implemented (a form of) end correction in some of their Synergy horns. The Equivalent Throat system is one of the few theories that includes end correction in the combined application of a compression driver + horn. The science behind the end correction is thoroughly adressed by Neville H. Fletcher and Thomas D. Rossing in "The Physics of Musical Instruments". The topic is also discussed in the works of: Beranek Howard and Craig Kurze and Riedel Junger and Feit Morse and Feshbach, Morse and Ingard and numerous others.
Hi Ro808,

Very nice presentation and and explanation.
So for the most of us understanding why some times resonance frequency of the bass-reflex box is not exactly on the 'desired' frequency, but fortunately, cutting some length of the vent(s) such problem would be 'solved'

Regards
ivica

tnargs
diyAudio Member

Join Date: Sep 2006
Quote:
 Originally Posted by gedlee A properly flared horn/waveguide will not have any significant "end correction". The concept is ill-applied to a good waveguide.
Thank you Earl.

On a different topic, my local horn manufacturer's chief designer recently told me that exponential horns still produce measured ripple when driven by a sine wavelength equal to the mouth circumference. Suggesting that the old linear model was inadequate.

 25th July 2018, 08:22 PM #14878 gedlee   diyAudio Member     Join Date: Dec 2004 Location: Novi, Michigan The old linear model has been known to be inadequate since I wrote my Waveguide papers in 1991. All horns/waveguides produce "ripple" - some much much more than others. It's all about the design: flare: termination: phase plug; lots of different things can cause this well know problem. __________________ Earl Geddes Gedlee Website
hollowboy
diyAudio Member

Join Date: Jul 2007
Location: 'straya
Quote:
 Originally Posted by tnargs my local horn manufacturer's chief designer
I'm curious about who this could be. I didn't know there was a non-hobbyist manufacturer in Australia.
__________________
This edit signature thingy is seriously hard to find

David McBean
diyAudio Member

Join Date: Jun 2007
Quote:
 Originally Posted by tnargs On a different topic, my local horn manufacturer's chief designer recently told me that exponential horns still produce measured ripple when driven by a sine wavelength equal to the mouth circumference. Suggesting that the old linear model was inadequate.
The plane wavefront model is not inadequate for the reason stated above. It predicts quite accurately the behaviour described, which is due to the acoustical impedance mis-match at the horn mouth. An acoustic "waveguide" also has an impedance discontinuity at the mouth.
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