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Just wave!

Just need substantiation on a speaker building point:

With a TL speaker, one of the main reasons for the transmission line is to reverse the polarity of the wave, off the back of the speaker, so that it will be in phase with the front of the speaker cone, when it exits the port.  Knowing the resonant frequency of the speaker and its wavelength, we them determine the length of TL which will allow the inverse of the back wave to be 'happening',...when it leaves the port?  To put it another way:  we are bouncing the wave within the TL until we are, essentially, releasing it....while it is in the proper orientation.  Is that correct?
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mjking57
14 posts
 
I don't know anything about the speaker measured or the measurement set-up, so my response is speculation. I have seen a similar notch in some of my measurements and have investigated the cause.

I don't believe any of the measurements that you have linked are for TLs, they appear to be bass reflex enclosures. I draw this conclusion from the electrical impedance plots where there are two almost equal peaks, one above and one below the tuning frequency, and no peaks from higher harmonics. If it was a TL and was stuffed to remove the higher harmonics then the lower impedance peak would also be strongly suppressed. If these speakers are not TL's then the cause of the null is not a cabinet standing wave resonance.

I measured a TL that exhibited a deep notch at a similar frequency to the one in your linked plots. I modeled the design and was able to reproduce the null. My initial thoughts were that the notch was created when the open end and the woofer were not at the same location (assumed in almost all simulation software) or from a room boundary reflection. I simulated both conditions and found that the floor reflection was the cause as sound traveling from the woofer to the floor, reflected, and then traveling from the floor to the mic causing it to arrive out of phase and cancel most of the direct sound from the driver to the mic.

That is my speculation.
audiokinesis
2,737 posts
 

Thank you for replying, Martin.

Those measurements were made in the anechoic chamber at the Canadian NRC, so I don’t think the notches are floor-bounce cancellations.

Both of the speakers in my links above are marketed as "transmission lines", and both are floor-standing two-ways with a small mid-woofer near the top and the terminus on the front near the floor.

https://pmc-speakers.com/products/archive/archive/gb1

https://pmc-speakers.com/products/consumer/twenty/twenty24

Does that shed any light on the source of the notch?

Also, could you clarify something you said for me?  "At frequencies where the TL enclosure is producing output from the open end the phase must be +/- 90 degrees with respect to the driver."

So is the output from the open end ALWAYS in phase quadrature with the output from the cone, regardless of the frequency? 

Or is it ONLY in phase quadrature at the quarter-wave resonance frequency? 

My apologies if I'm asking something that should be obvious.

Thanks!

Duke

mjking57
14 posts
 

Assume we have a driver with an fs of 50 Hz and it is installed at the closed end of a straight TL tuned to 50 Hz, the simplest form of TL design. The TL will produce standing waves at the 1/4, 3/4, 5/4, … frequencies of 50 Hz, 150 Hz, 250 Hz, … as expected. Neglect the acoustic impedance at the open end or terminus and assume the TL is completely empty so there is no damping of any kind. At a standing wave resonance, the back pressure on the driver cone will attenuate the motion, almost stopping the driver like in a BR design, and almost all of the SPL output will be from the terminus, like the port in a BR enclosure. The SPL and phase of the outputs will behave as follows.

Well below 50 Hz – as the driver moves into the TL it displaces a volume of air and an equivalent volume of air is pushed out of the terminus. The driver and the terminus are 180 deg out of phase and the SPL almost cancels producing a 24 dB/octave roll-off below 50 Hz.

At 50 Hz – the 1/4 fundamental standing wave is excited, the driver motion is significantly attenuated, and most of the SPL output comes from the terminus. The driver and the terminus are 90 degrees out of phase.

At 100 Hz – the driver and terminus are now in phase. There is no standing wave and the SPL from the driver and terminus are equal. This is because sound radiated from the back of the cone is the same as from the front of the cone but 180 degrees out of phase, the sound traveling down the TL is constrained so it does not decrease with distance, and the distance it travels is equal to a half of a wavelength (another 180 degrees). Theoretically, the system SPL will be 6 dB greater than the driver’s SPL in an infinite baffle.

At 150 Hz – the 3/4 standing wave is excited, the driver motion is again significantly attenuated, and most of the SPL output comes from the terminus. The driver and the terminus are 270 degrees (-90 degrees) out of phase.

At 200 Hz – the driver and terminus are now out of phase. There is no standing wave and the SPL from the driver and terminus are equal. This is because sound radiated from the back of the cone is the same as from the front of the cone but 180 degrees out of phase, the sound traveling down the TL is constrained so it does not decrease with distance, and the distance it travels is equal to a full wavelength (another 360 degrees). The driver and the terminus are 180 deg out of phase and the SPL almost cancels producing a deep null, maybe this is what the measurements are showing.

The phase and SPL pattern repeat as frequency increases and moves through the higher quarter wave frequencies. Below is a list of key frequencies and the phase differences between the driver and terminus.

10 Hz – 180 deg SPL --> 0 dB

50 Hz – 90 deg fundamental 1/4 wave and SPL mostly from terminus

100 Hz – 0 deg SPL + 6 dB

150 Hz – 270 deg (-90 deg) 3/4 wave and SPL mostly from terminus

200 Hz – 180 deg SPL --> 0 dB

250 Hz – 90 deg 5/4 wave and SPL mostly from terminus

300 Hz – 0 deg SPL + 6 dB

350 Hz – 270 deg (-90 deg) 7/4 wave and SPL mostly from terminus

400 Hz – 180 deg SPL --> 0 dB

The pattern repeats in steps of 50 Hz. I hope that is clear.

 


audiokinesis
2,737 posts
 

Thank you very much Martin for taking the time. Your last post makes sense to me.

I was having a hard time with the second half of this sentence:

"You cannot produce a half wave resonance and the output will never be in phase with the driver output. "

But this from your last post makes sense to me:

"At 100 Hz – the driver and terminus are now in phase."

So at 100 Hz (where the line length is equal to 1/2 wavelength) there is NO standing wave resonance, BUT the outputs from the driver and terminus are IN PHASE.

Have I finally got that right?

And "At 200 Hz – the driver and terminus are now out of phase."  (But there is no standing wave resonance.)  So IN THEORY at least, assuming a lightly-damped line, couldn't we get a cancellation notch in the summed response in that region?

Duke


mjking57
14 posts
 
You have it correct. And in theory, yes a notch could be produced. But the minute you add back in the damping produced by the acoustic impedance of the terminus, add fiber or foam damping in the line, place the driver along the line instead of at the closed end, and account for the offset positions of the driver and terminus on the baffle the sharp peaks and deep nulls start to smooth out. The terminus output between the 1/4 wave resonances starts to be attenuated and the phase shifts a few degrees so the reinforcement and cancelling is not as dramatic. You start to get the rippled rolling frequency response typically associated with TLs.

Thinking about the measurement plots you linked, if they have designed a TL that when damped still has a deep notch at a frequency around 200 Hz, between the 1/4 wave resonant frequencies, when measured in a chamber with no boundary reflections then the design needs further work in my opinion. The damping does not appear to be very effective below a few hundred Hz. In a correctly damped TL, tall peaks and deep sharp notches should not occur. Usually you are left battling the ripple and use driver offset to tame it.
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