1/4, 1/2 wave lengths and so on

[The Dude]

What does this stuff mean. I know I should just stick to what works, but whats the fun in that. I have been reading about mixing and matching speakers, horns, drivers, etc.. But have this stuff kind of goes in one ear and out the other. I know if I try sometimes and read things over and over eventually I will get it. Does anyone have any layman's terms to understanding this stuff. I kind of am understanding off axis I just don't know where the axis is located(if that makes since). I under stand wanting to cover frequency ranges, that seems to be the easy stuff. Then you go into crossover design with 1st 2nd third and so on, that all just gets confusing seems knowing what to try with a active crossover would be a easier way to go. Then you get into horn design and all that jazz. I guess I am kind of a hands on learner, sometimes I need some one here to point that out so I can understand it. Anyone want to stop by and give me a education on this stuff, I don't know maybe its a lost cause but will I give no sir, or mam. Thanks to all who help.

[WMcD]

What does this stuff mean. I know I should just stick to what works, but whats the fun in that. I have been reading about mixing and matching speakers, horns, drivers, etc.. But have this stuff kind of goes in one ear and out the other. I know if I try sometimes and read things over and over eventually I will get it. Does anyone have any layman's terms to understanding this stuff. I kind of am understanding off axis I just don't know where the axis is located(if that makes since). I under stand wanting to cover frequency ranges, that seems to be the easy stuff. Then you go into crossover design with 1st 2nd third and so on, that all just gets confusing seems knowing what to try with a active crossover would be a easier way to go. Then you get into horn design and all that jazz. I guess I am kind of a hands on learner, sometimes I need some one here to point that out so I can understand it. Anyone want to stop by and give me a education on this stuff, I don't know maybe its a lost cause but will I give no sir, or mam. Thanks to all who help.

It Is a lot to explain, especially without pictures.

If you are "on axis" you are perpendicular to the front baffle of the speaker box, generally. You are looking down the throat of a straight horn. You are perpendicular to the disk of a direct radiator diaphragm. Of course you can't be on axis to all the drivers because they are spaced.

If you move perpendicular and are looking at the side of the box, you are position\ed 180 degrees off axis.

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You can check Wikipedia and the web for wavelength. Look at the pictures and ignore the math, at first.

The most common way to consider the wavelength of a sine wave is to look at a diagram.

It starts at zero amplitude. It goes up to a peak. That peak is 1/4 wavelength. Or 90 degrees of the cycle.

Then it goes down to zero amplitude. That is 1/2 wavelength. 2/4. or 180 degrees of the cycle.

Then it goes down to a negative valley and the bottom is 3/4 wavelength or 270 degrees of the cycle.

Then it goes back up to zero. That is a full wavelength or 4/4 wavelengths. 360 degrees of the cycle.

You'll notice that if you add up the peak and valley, the sum is zero. That means there is no overall movement of air or overall change in pressure(which would be more like wind from a fan).

Wavelength and frequency are reciprocals. Higher frequency, smaller wavelength. The speed of sound is constant (for our purposes). But the rate that the plus and minus go by and into your ear changes. Smaller wavelength, the plus and minus occur more quickly as the wave travels at a constant speed.

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You can estimate the frequency to wavelength.

A 1000 cycle per second frequency is called 1000 Hertz (named after the physicist). It completes its up and down cycle in 1/1000th of a second.

A 1000 Hz audio wave in air has a wavelength of about 1 foot. (Actually a bit more, but let's not let exactness get in the way of understanding.)

A 2000 Hz audio wave in air has a wavelength of 0.5 feet.

A 4000 Hz wave has a wavelength of 0.25 feet.

Going down from 1000 Hz.

A 500 Hz wave has a wavelength of 2 feet.

A 250 Hz wave has a wavelength of 4 feet.

You can see the doubling and halving.

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Waves, including sound, can and do add, in effect(s). But notice that sometimes the wave is negative in amplitude and it is helpful to consider this to be pressure relative to ambient atmospheric pressure. The zero is actually atmospheric pressure. (Technically pressure is where the air molecules are bunched together and want to spring apart. When they spring apart they cause "volume velocity" which is like cubic inches per second. This volume of air movement sloshes back and forth responding the continually reversing pressure, so there is no net displacement of air in a full cycle. Sort of like reversing mini-winds).

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Maybe this is getting too complicated but . . . Often we consider electrical circuits and the first analysis is direct current (d.c) which is really to say, unchanging voltage from a battery. If you have a two cell flashlight . . . and put the batteries in head to toe, the voltages add in "series". The 1.5 volt batteries add to make 3.0 volts to drive the bulb.

But if put one in backwards, there is still a series circuit but one battery is essentially a source of equal negative voltage. The "add" in the sense that one battery drives the voltage up in the loop, but the other drives the voltage down. The bulb gets zero voltage -- all the time.

But suppose you have a three cell flashlight where the bulb expects 4.5 volts. And you put one cell in backwards. Now with our addition rule, we get 1.5 volts at the bulb -- all the time. The backward negative voltage battery has cancelled out the effect of one of the other proper batteries.

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I bring up the important "all the time" issue of unchanging voltage at the battery terminals. In alternating current analysis (a.c.) we have what is better called alternating voltage of the sine wave (plus and minus over a single wavelength or cycle and we usually think of many many cycles). That is true of sound waves too.

So we have to look at adding two sine waves of the same frequency and therefore wavelength. Unlike the battery, the voltage or air pressure is always changing. About all we can do is graph the sine wave of one and overlay the sine wave of the other and see how they add.

The easiest is when both are "in phase" and the peaks and valley of each occur exactly the same. The add to twice the pressure peak or valley.

If the second one is exactly the reverse they add to zero. This is also called 180 degrees out of phase. (Don't confuse this with the 180 degrees off axis thing.) Then they add to zero. Of course we can have a situation similar to the three cell flashlight where the voltages or pressure add to partially cancel, even if they are in phase.

Consider when the sine waves are 180 degrees out of phase relative to each other (one started from zero a half wavelength later or 180 degrees later. Now if they are equal in heights and depths they cancel - all the time. This is called a null. Total cancellation all the time. This is why you read that waves which are 180 degrees "out of phase" cancel. Actually, in the science, we try to use one wave as the reference and say that the second has this or that phase relative to it.

Now it gets complicated. We can also let the second wave start, say 90 degrees later in its climb to the first peak and the peaks and valley of the second is not as high as the first sine wave. They both have the same frequency and therefore wavelength (but their zeros and peaks don't match over time. We have to make the two graphs and add up all the points on the two graphs.

What comes out of the sum? It is a head scratcher.

One almost magical result is a sine (or sinusoidal) wave. It has the same shape overall as the two (same freq and wavelength) which made it. You may say you know this because if two speakers are sending out the same musical note / wavelength / frequency, there is not a different musical note.

But it has a different phase relative to either of what make it up. And the overall amplitude has changed (if they're 180 degrees out of phase with each other, the sum is zero). The exact amplitude takes more math.

= = = =

I went far afield here, but this is why wavelength and phase must be studied. The second sine wave in our studies of room acoustics is usually reflections off the walls ceiling and floor. A real "ear opener" is to play a single tone (sine wave of a freq through one of you speaker of about 200 Hz and walk around the room. It is astonishing to find that at some locations, there is silence. This is the summation of all (at least at your ear) to zero. At other locations we hear a tone of some level. That we hear something is the phenomenon of "standing waves".

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I've mention magic of sine waves in adding. There is more magic and we have to keep with a pure sine wave.

You may have read that capacitor and inductors have current and voltage relations which rely on the integration or differentiation of the sine wave. Calculus.

The integration means adding up all the sine wave which have gone before and are still going on. It is interesting that this ongoing sum (travelling average) is a sine wave of the same frequency. Different phase.

The differentiation means that we take the slope of the sine wave. this again results in a sine wave of the same freq. Different phase.

This different phase is why you see descriptions of lead or lagging in phase and is described with "j".

= = = = =

Okay, I went overboard here. The whole freq and wavelength thing is needed to understand room acoustics and adding.

The sine wave or "one freq" analysis lets us look at calculus as simply a matter of phase and amplitude.

WMcD

[mustang guy]

Thanks for the explanation. I learn so much from you!

I am like Duder, a hands on learner... Here are a couple things I figured out and found interesting. The math to figure out a wavelength is the speed of sound divided by the frequency. Sound is 1125 feet per second at room temperature and at sea level. If you want to calculate the waveLENGTH of 27 Hz, just take 1125 (sound fps) divided by 27 (Hz) and you get 41' 9". Another thing I found out was that horn loaded speakers typically have a horn length of 1/4th of the tuned frequency. That is to say that the length of a horn tuned to 27 Hz would typically have a horn length (if you could unfold it and measure it) of one forth of 41' 9" = 10' 5-1/4". I also understand that you could make a full horn by having a horn length of the full 41 9" or a half horn which would measure 20' 10-1/2". That is how I understand it in layman's terms.

If I misunderstood something, please correct me, so I can correct this post so as not to mislead everyone.

[The Dude]

William thanks for the explanation, though you lost me after the battery part. I will have to (like I said read it a thousand times and play with it to understand it)..

Mustang I like your explanation as well, something I didn't know. Still will have to think for a bit to understand fully but its kind of bringing things together. I get kind of excited when I start to understand something. I wish times like this we had a chat room.

[The Dude]

How about this to make a tube a 1/4 wave length of the first high impedance peak of a Faital Pro hf200 would be. Wait lets back up the first high impedance peak of the driver is around 550 hz so 550 hz divided by 1125 would be 2.04ish. Then a quarter wave length would be .511 ish now is that in inches or feet so that should be about 6" or so.

[derrickdj1]

This was an excellent post and answer. It was very informative. Thanks guys!

[djk]

Fig. 5.11A is the same as 5.10B

Fig. 5.10 shows the effect of mouth area of a family of 100hz taper horns.

Fig. 5.10C or D? C is the minimum I would consider acceptable from a ripple standpoint (a 2:1 ratio in impedance is about a 6dB envelope). D is better, but getting large.

Note: an infinitely large mouth (fig.E) has no output at the cut-off frequency, but it has no ripple either.

With respect to Fig.5.10, what is a LaScala?

Translated to circular area it is about 27", or close to Fig.5.10C

Fig.5.11 shows the effect of using a larger throat and trying to make the horn shorter.

Fig.5.11C is about 1/4W of 100hz, note how it cuts off below about 150hz. The LaScala is about 36" deep, and in Hornresp it starts to roll below the peak around 140hz.