Hi Guys. I'm interested in your views here on a subject that may be quite relevant to those designing tall, thin floor-standing speakers.
Say we take a sealed box design and stretch it while keeping the volume constant so that it becomes taller and less deep and wide. When does it start to act like a closed transmission line?
Say we take a sealed box design and stretch it while keeping the volume constant so that it becomes taller and less deep and wide. When does it start to act like a closed transmission line?
Do you lie awake at night thinking of questions like this? I don't know. Are we talking about setting up a 1/4 wave inside the enclosure? What happens with the pressure changes? 
Hi Steve,
I assume you are talking about a closed ended transmission line which exhibits half wavelength standing waves. If that is the case, then I think the answer to your question is that all closed boxes are transmission lines. The real question is at what frequency the transistion from a lumped parameter closed box model to a standing wave closed box model occurs. This is determined by the longest dimension of your closed box.
f = c / (2 x L)
So as length increases, the frequency at which the first standing wave occurs decreases. You can calculate this frequency for all three dimensions of a rectangular closed box.
The next problem is how much do the standing waves impact the driver SPL response. This will be determined by the position of the driver along the length and it may be that it is not until you excite the higher order standing waves that problems occur. Also, closed boxes are typically stuffed so any standing waves will be damped. My MathCad worksheet "Closed Box" does this type of simulation for one dimension.
Hope that helps,
I assume you are talking about a closed ended transmission line which exhibits half wavelength standing waves. If that is the case, then I think the answer to your question is that all closed boxes are transmission lines. The real question is at what frequency the transistion from a lumped parameter closed box model to a standing wave closed box model occurs. This is determined by the longest dimension of your closed box.
f = c / (2 x L)
So as length increases, the frequency at which the first standing wave occurs decreases. You can calculate this frequency for all three dimensions of a rectangular closed box.
The next problem is how much do the standing waves impact the driver SPL response. This will be determined by the position of the driver along the length and it may be that it is not until you excite the higher order standing waves that problems occur. Also, closed boxes are typically stuffed so any standing waves will be damped. My MathCad worksheet "Closed Box" does this type of simulation for one dimension.
Hope that helps,
Martin:
In your equation:
f = c / (2 x L)
Does "c" stand for the speed of sound per second, which is 13,500 inches?
In your equation:
f = c / (2 x L)
Does "c" stand for the speed of sound per second, which is 13,500 inches?
Excellent Martin, thanks. I thought that was the case. I'll compare your MathCad to some measured results that I have and see what I get.MJK said:
Of course I do. 🙂 Obsessed or what?
BTW, is anyone going to be at the Bristol Show next month? I'll be exhibiting there.
Hi keltic wizard,
Yes, c is the speed of sound. Actually to keep the units straight and get the answer in Hz, it would probably be better to do the following calculation.
f = (2 x pi x c) / (2 x L)
When I use MathCad it keeps the units straight for me so I tend to not pay attention. If you are using a calculator the formula above results in the correct units of Hz.
Yes, c is the speed of sound. Actually to keep the units straight and get the answer in Hz, it would probably be better to do the following calculation.
f = (2 x pi x c) / (2 x L)
When I use MathCad it keeps the units straight for me so I tend to not pay attention. If you are using a calculator the formula above results in the correct units of Hz.
Martin:
Thank you.
Just one more question. In the equation:
f = (2 x pi x c) / (2 x L)
Does pi stand for pi, (3.14), or some other number?
Thank you.
Just one more question. In the equation:
f = (2 x pi x c) / (2 x L)
Does pi stand for pi, (3.14), or some other number?
kelticwizard,
Right again, I am not having a good day at the keyboard.
ph = 3.14159265........
Maybe I should give it a rest and take a nap. Audrey is taking the kids out to the mall, I know I probably have something I am supposed to be doing .... but a nap sounds good.
Right again, I am not having a good day at the keyboard.
ph = 3.14159265........
Maybe I should give it a rest and take a nap. Audrey is taking the kids out to the mall, I know I probably have something I am supposed to be doing .... but a nap sounds good.
kelticwizard,
Looks like I have screwed up the units again.
L = c / (4 x fd)
so if
c = 344 m/sec
fd = 50 Hz
L = 1.72 m = 67.7 in
The simple stuff is my downfall. This has been nagging at me since I wrote the initial reply. But once I got back to work today, I had some time to resolve it. Gotta go here comes the boss ....
My appologies,
Looks like I have screwed up the units again.
L = c / (4 x fd)
so if
c = 344 m/sec
fd = 50 Hz
L = 1.72 m = 67.7 in
The simple stuff is my downfall. This has been nagging at me since I wrote the initial reply. But once I got back to work today, I had some time to resolve it. Gotta go here comes the boss ....
My appologies,
So, fd = c / (4 x L).MJK said:
So does this refer to open lines and c / (2 x L) to closed lines?
And what happened to pi?
7V said:
The simple answer is it depends on the amount of acoustic
damping in the speaker. For a closed box you stuff it completely.
A more interesting question is tall and thin reflex speakers,
where total stuffing is not an option, standing waves and
port placement then become an issue.
🙂 sreten.
Steve,
L = c / (4 x f) is for open ended TL's
L = c / (2 x f) is for closed ended TL's
The 2 x pi term gets into the mix when you express freqency in terms of rad/sec instead of cycles/sec. One cycle is 2 x pi radians.
Where I got mess up was I forgot that MathCad converts frequency to rad/sec even if you enter Hz. So I was double checking using MathCad and forgot about the internal conversion. Units will hang you everytime in a calculation if you don't pay careful attention.
L = c / (4 x f) is for open ended TL's
L = c / (2 x f) is for closed ended TL's
The 2 x pi term gets into the mix when you express freqency in terms of rad/sec instead of cycles/sec. One cycle is 2 x pi radians.
Where I got mess up was I forgot that MathCad converts frequency to rad/sec even if you enter Hz. So I was double checking using MathCad and forgot about the internal conversion. Units will hang you everytime in a calculation if you don't pay careful attention.
>The simple answer is it depends on the amount of acoustic
damping in the speaker. For a closed box you stuff it completely.
====
A little too simple for me. 😉 Some drivers work best with stuffing, but many don't, so the driver's location along the line is key to getting a smooth FR, just like in a ML-TL.
====
>A more interesting question is tall and thin reflex speakers,
where total stuffing is not an option, standing waves and
port placement then become an issue.
====
While total stuffing is beneficial with certain drivers, you're right that in most cases it should be kept to a minimum and smooth the FR with driver/vent placement.
GM
damping in the speaker. For a closed box you stuff it completely.
====
A little too simple for me. 😉 Some drivers work best with stuffing, but many don't, so the driver's location along the line is key to getting a smooth FR, just like in a ML-TL.
====
>A more interesting question is tall and thin reflex speakers,
where total stuffing is not an option, standing waves and
port placement then become an issue.
====
While total stuffing is beneficial with certain drivers, you're right that in most cases it should be kept to a minimum and smooth the FR with driver/vent placement.
GM
- Status
- Not open for further replies.