QWT - opened and closed case

[weinstro]

Hi All,

If I have a transmission line, with a loudspeaker on one end, and open on the other, is this considered to be a QW pipe, or will it resonate at half-wave lengths? Would this be properly called an open or closed pipe? IOW, is the end with the speaker on it considered to be open or closed?

If the far end is closed, same questions as above?

Thanks!

[kelticwizard]

On the open end question, it is indeed a quarter-wave pipe. It will resonate at quite a few points up the scale above the quarter wave as well.

Martin J. King has a special worksheet specifically made for this case, as well as many other quarterwave pipes, open and closed boxes. www.quarter-wave.com

[MJK]

If I have a transmission line, with a loudspeaker on one end, and open on the other, is this considered to be a QW pipe, or will it resonate at half-wave lengths? Would this be properly called an open or closed pipe? IOW, is the end with the speaker on it considered to be open or closed?

the simplified answer follows. The speaker end is considered to be a closed boundary condition. The open end is considered to be an ........ open boundary condition. This means that quarter sine and cosine waves are the fundamental air velocity and pressure profiles along the length. At a closed end, the velocity is zero and the pressure is a maximum. At an open end, the velocity is a maximum and the pressure is zero. For a TL of constant area, the standing waves will occur at approximately the following frequencies.

f = n x (c / 4 L)

where

c = speed of sound
L = length
n = 1, 3, 5, ... odd integers

If the area tapers or expands along the length, the relationship above does not hold. This is the most common mistake DIYers make when deciding on the length of a tapered TL.

If the far end is closed, same questions as above?

If the end opposite the driver is closed, then this is a closed-closed TL. The standing waves will be half wavelength sine and cosine profiles for velocity and pressure respectively. The pressure will be a maximum at each end and the velocity will be zero. For a TL of constant area, the standing waves will occur at approximately the following frequencies.

f = n x (c / 2 L)

where

c = speed of sound
L = length
n = 1, 2, 3, ...

The same warning as above applies when calculating the length of a tapered or expanding TL.

This is the simplistic explanation of a TL and the resonant frequencies and associated standing waves. For a more complete explanation my anatomy of a TL article is a better discussion (but possibly not understandable).

[weinstro]

Originally posted by MJK
the simplified answer follows. The speaker end is considered to be a closed boundary condition. The open end is considered to be an ........ open boundary condition.

OK, that helps clear up one point of confusion I had.

If the area tapers or expands along the length, the relationship above does not hold. This is the most common mistake DIYers make when deciding on the length of a tapered TL.

Ahhh, OK. I have a follow-up question. I've borrowed texts by HF Olson and M Collum on acoustics, which cover the situation of acoustic impedance as a function of change in cross sectional area. Let me propose some additional conditions:
1. the pipe is closed at the far end, but opens into a plenum behind the driver. The cross sectional area of the plenum is larger than that of the pipe, by perhaps 5x.
2. the length of the pipe corresponds to a resonant frequency equal to that of the driver's Fs
3. The volume of the plenum and the pipe just happens to correspond to the volume predicted by one of the many box design programs to equal a Qtc of 0.707.
4. The volume of the plenum is big enough to house the driver, but not much bigger than that

Under these conditions, am I looking at a quarter wave pipe, a half wave pipe, or something else?

Thanks!!

[MJK]

If it is closed at the far end, then I would say you are looking at a form of half wave pipe.