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The Mechanics of a Loudspeaker

The cross section of a Loudspeaker

The cross section of a Loudspeaker

In the last loudspeaker post, “The Electrical Part of a Loudspeaker” we “divorced” the mechanics from the electrical part of the speaker.  But like good divorce judges we are now going to listen to the other side of the story.  The picture to the left shows a cross section of a loudspeaker and these parts were fully described in the post “Our first Motor – A Loudspeaker“.  Mechanically, we have lots and lots of problems to think about while we are trying to “pump air”.

The first problem is getting a handle on what sound is and our goal of being able to accurately reproduce it.  Our ears are amazing sensing organs because of the range of sounds we can hear.   Sound is measured in pressure per square meter and 0 dB SPL (Sound Pressure Level) was assigned to just perceptible sound.  At 85 dB SPL is considered loud enough to cause hearing loss if experienced for a full 8 hour working shift. 120 dB is considered to be the threshold of pain.   Remember, 10 dB increase is a 10 fold increase in power.  This means a 90 dB sound is 1,000,000,000 times more powerful than a 0 db sound.   That is a bunch!

The frequencies we can hear is almost as amazing.  The range of hearing is commonly considered to be from 20 Hz to 20 KHz.  Lets do some quick calculations.   The wavelength of a sinusoidal sound wave is the distance it travels from one peak pressure excursion to the next peak.  The formula for wavelength is:  wave speed X time per cycle  which becomes: the speed of sound / the frequency of interest.   The speed of sound in dry air at sea level at 20°C is 343.2 meters/second or 1,126 ft/s. The calculations give us the following table.

Frequency Wavelength (English) Wavelength (Metric)
20 Hz 56 ft 4 in 17.16 meters
200 Hz 5 ft 7 in 1.716 meters
2000 Hz 6.75 in 17.16 cm
20 KHz 0.675 in 17.16 mm

Remember we referred to the diameter of the cone as the “piston diameter”. If we wanted the piston diameter to be equal to 1/2 wavelength. we would have to have a very big speaker for the low frequencies and a very tiny one for the highest frequency…. Not going to happen! However, this does explain why most speaker systems contain several speakers.  Usually these are referred to as a wolfer, a mid-range, and a tweeter.  I looked up a speaker of each type from an electronics web site and got this data.

 

Speaker Type Diameter (English) Diameter (Metric) Frequency Range
Wolfer 12 in 30.48 cm  26 to 3000 Hz
Mid-range 4 in 10.16 cm 700 to 10,000 Hz
Tweeter 1 in 25.4 mm 1500 to 20,000 Hz

This makes an interesting situation. The Wolfer is less than 1/50 of the lowest frequency wavelength and the tweeter is about 1.5 times the wavelength of the highest frequency.  This creates two problems.  First, the Wolfer will have a create a sound wave that is not directional, like throwing a rock in a pool, where the tweeter will be very directional and will have to be aimed toward the listener.  The 2nd problem is more interesting to us right now.  To produce the same pressure the wolfer will have to have a larger stroke than the tweeter or mid-range since it is a much smaller area compared to the wavelength.

Most of the design work I have seen done on speakers is associated with the low frequencies.  Because the Wolfer must move so much air, the cone needs to be stiff to not flex.  Stiffness and size adds weight.  This means we have a weight attached to a spring, the spider,  Just like my hammer attached to the rubber band video, this is probably going to tend to oscillate as some frequency and that could lead to some “booming” at that frequency.  Also the weight is why the wolfer has a limited high frequency.  It is just too much weight to move quickly.

There is an additional problem.  So far we have pretended that the back side of the cone does not exist, but it does exist and it also acts like a piston.  The problem is that while the front of the speaker is compressing air, the back side is creating a vacuum.   In the case of low frequencies these have time to react to each other and cancel.  The first answer to this problem is mostly a theoretical answer called the infinite baffle.  Infinite is pretty big and not too practical to build.   However, you probably could mount the speakers in an outside wall, it probably would not make the neighbors happy, but you could do it.   The more practical approach was to mount the speakers in a box and do something with the sound from the back side.  A speaker design called bass reflex tries to combine the sound from the back of the speaker so it reinforces the sound from the front.   The problem with this is it is very hard to tune so the speaker is not “boomy” at some frequencies.  Various things are tried including making the port out of a pipe that reaches well into the box.   Sometimes this pipe is fitted with a diaphragm to dampen the sound from the back and sometimes there are small tubes placed in the pipe to help tune it.

Another design that was popular uses a closed box that is sealed and usually some kind of sound dampening material inside the box.   The goal of this design called acoustic suspension is to have the air act like a spring so the spider spring can be made weaker.   This provides a much more linear spring than the mechanical spring and allows for a longer speaker throw.

Other mechanical issues that have to be thought about and dealt with is the extreme flexing of the surround flexible material.   Also some thought must be provided to removing heat built-up in the voice coil windings.   From what I understand this is actually a bigger problem in tweeters than it is in the other speakers because of the very high vibration rate.  These problems are dealt with by the actual speaker manufacture and are not of concern to someone building the enclosure except in the choice of the speakers to specify.

All in all speaker enclosure design is a complicated subject and requires some equipment to test the speakers.   I have build a few enclosures but I pretty much gave up on trying to do all the design and much of it looks like a combination of black magic, experience, and a whole lot of marketing.   The enclosure I built was for my son’s car when he was a teeenager and wanted a “system” in his car.   While it probably did not meet audiophile expectations, it did put out a lot of sound and when the rear-view mirror vibrated so much that the headlights of cars behind us looked like circles, he was very happy.   At least it did not sound like “Godzilla Thumping” like many of the car audio systems do.

There will probably be one more Loudspeakers post.   In that post I will provide a lot of links where you can look at some various D.I.Y. designs and construction as well as a lot more detailed theory.   I will also mate the Electrical and Mechanical systems

As always, I hope this was enjoyable and entertaining.    Gary

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