A TL that is closed at one end and open at the other always produces a quarter wave standing wave resonance. It does not matter where the driver is along the length or if the geometry is tapered, straight, or expanding. Always a quarter wave. This means that at frequencies where the TL enclosure is producing output from the open end the phase must be +/- 90 degrees with respect to the driver. No matter what the physical length, the resonant frequency will be produced by a quarter wave resonance. You cannot produce a half wave resonance and the output will never be in phase with the driver output. Unfortunately that violates the laws of physics.
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?
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 - Thank you Martin, apparently I have some misconceptions. I hope you don’t mind if I ask a question or two. I recall many of my primitive transmission lines of yesteryear having a distinct notch in the response that seemed to correspond with a line length of one wavelength. You can see what I assume is the same sort of notch in these measurements: https://www.soundstage.com/measurements/pmc_gb1/ https://www.soundstage.com/index.php?option=com_content&view=article&id=775:nrc-measurements... What’s causing that notch? Thanks, Duke |
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. |
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 |
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.
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