Analyzing the decibel output of a speaker operating at various frequencies while manipulating the port length

 

Return To Research:                                      By: Cam Chase & Grant Chaput

Background Information:

            Many people are deceived by the desire for a bigger better speaker. Contrary to popular opinion, a powerful driver cannot do the job alone. Loudspeakers, in actuality, are heavily dependent op their enclosures.  There are various types of boxes that can make or break the response of a speaker.  Most of those various types of boxes come equipped with a port to increase the speaker’s bass response.  Speakers offer better response at different ranges of frequencies.  There are subwoofers, woofers, mid-ranges, tweeters, and supper tweeters which are listed in order from lowest to highest frequency response.  Whereas, a tweeter will not play a 50 Hz tone, a subwoofer will; and a woofer will not play a 2600 Hz tone, a supper tweeter will.  Likewise, venting, or lack there of, along with size of the vent, contribute to the output response of the speaker.

 

The Problem:

 

            The purpose of this study is to determine how to create a loudspeaker system that is small in size, while maintaining high decibel-output levels.  Louder is better, smaller is cheaper, how do you achieve high decibel output levels, while maintaining a minimum size?

 

Review of Related Literature:

 

                Early attempts at vented speaker boxes were not refined, and consequently few were successful.  However, those that worked were more efficient and had better bass response than comparable closed-box enclosures (Kauffman 121).

 

The most common type of port is a round tube. These are typically made of black plastic and look like a section of thin-walled pipe with a lip on one end. The second most frequently used type of vent is a square port. The advantage of this design is that you are not limited by availability of only certain diameter tubes. You can also build the port out of the same material you are using to fabricate the enclosure. The last type of port is called a slot port. It is created using one wall of the enclosure as a wall of the vent. This can be very useful for bandpass enclosures, which can be very hard to tune to a low enough frequency due to the small size of the front (vented) chamber (Westenkow).

 

            Each Driver differs slightly in its parameters such as the sharpness of resonance and resonance frequency of the driver.  This difference in drivers makes it necessary, in order to obtain optimum speaker performance, for each unique driver to have a customized enclosure.

 

            Vent length is very important to the speaker enclosure, the necessary length can be found by using the formula (Kauffman 130):

 

LV = SV/(0.00037VBFB2) - .83V SV

 

where

            LV = Vent length, in inches

            SV = Vent area, in square inches

                FB = Box frequency

                VB = Box volume, in cubic feet

 

            Some experts believe that the length of the vent should not be larger than twice its diameter.

 

Hypothesis:

           

            The optimum port length is twice the diameter of the port opening.  The loudspeaker will have optimum decibel output when operating under 100 Hz.  A decibel meter will measure the decibel output, and the frequency will be kept constant by computer.  For our purposes, a 3” diameter round vent at various lengths will be used.        

 

Method:

 

            Knowing that the range of frequencies we tested were towards the bottom of the spectrum, 50-150 Hz, we used an 8” woofer which provided response in that range.  The box enclosure was made of dense pressboard with two holes, one for the port and one for the speaker.  The pipe we used is a low grade PVC pipe frequently used for water drainage.  We amplified the sound produced by Winamp using a Pioneer 100 Watt Receiver.  Other insignificant materials we used were earplugs, Jackets, and you can see in our diagram, some weird speaker wire.  

 

            First of all, knowing that we needed a controlled area in which to perform our experiments, we attempted to the best of our ability to insulate Cam’s room.  We tipped my mattress up against the wall and mounted the speaker about a meter from it.  Hopefully, the mattress acted as a sound dampener.  Eventually, virtually the only sound that was present was the low serenade of the computer fan.  And the rain, but we live in Oregon so we figured that that was a control.  It all worked out though because it doesn’t rain every day in Oregon, pretty darn close though.  Along with a controlling the environment, we were also able to control the frequencies at which we tested our speaker.  The frequency control was made possible by the wonderful people Nullsoft.  You see, Winamp has a frequency generator plug-in, we simply typed in tone://(your tone here) and Winamp played (your tone here) Hz.

 

            Our experimental setup contains 5 parts.  An easy way to show you the parts is by describing the route of the sound.  First, the computer generates a tone through Winamp.  That tone is routed by the sound card into the stereo.  The stereo was used solely as an amplifier, the volume level of which was kept constant throughout.  Following its amplification, the tone is sent to the speaker which physically created the sound.  The tone then escapes through a port of variable length and diffuses into the room.  Being located .5 meters from the speaker, the decibel meter measures the amplitude of the sound.  Port lengths, frequencies, and location of the decibel meter were all determined by a combination of logic, pre-experimental observations, and audibility.

 


            The decibel output of the speaker served as our dependent variable, which we measured with a decibel meter.  In obtaining different readings for each port length, we checked a variety of different low-end frequencies, starting at 50Hz, and going up to 150Hz, by increments of 5Hz.  One of us operated changed the frequency while the other sat behind the decibel meter relaying the meter’s readings to the other person who recorded the data.  We noted the reading on the decibel meter at each specified frequency, for all five port lengths.

 

Results:

            The following graph illustrates the Decibel output read by the meter.  As you can see from analyzing each of the lines, they all are related in shape, minimums and maximums occurring at the same frequencies.  The unique attribute of this graph is how the lines are inverted at 80 Hz, suggesting that the presence of the port begins to have little importance to the decibel output. 

 

Graph Data

            The following graph shows the average decibel output of the speaker.  As you can see, the port length which is the same as its diameter has the greatest average output

Graph Data

            The following graph illustrates the change in average decibel output caused by adding length to the port.

Graph Data

            As much as we would like to think we are well established, highly esteemed scientists, we’re not.  Consequently, we have quite a large amount of uncertainty.  The main cause of our uncertainty is most likely simple human error.  For instance, when the person running the decibel meter would move, the reflection of sound altered the readings.

            Interference refers to what happens when two waves pass through the same region of space at the same time.  As the decibel meter’s operator moved around, the medium reflecting the sound waves changed.  The angle of the medium directly affects the location of constructive interference and destructive interference.  If the input of the decibel meter happened to fall into an area of interference, the movement would affect the decibel meter’s readings.  As you can see in the following diagram, when the waves return towards the decibel meter after reflecting off of the chest of the decibel meter’s operator, destructive and constructive interference is created.  The constructive interference areas are more intense and the destructive interference areas are less intense than the non-conflicting areas.

            This principle also contributes to more uncertainly due to the fact that different frequencies have their own wavelengths.  As the wavelengths change in length, so do the locations of constructive and destructive interference.  This uncertainty partly constitutes the wave like pattern of the decibel output graph.

 

            The degree of human error involved, unfortunately, is virtually immeasurable though.  Other factors that contributed to our uncertainty are ambient noise, the resonance of the speaker box, and the fact that at about 70 Hz, Cam’s room seems to resonate quite well, you see, CDs and other various objects that a high school senior might have in his room began to shake—quite violently in fact, I’m serious, one CD even fell and cut my eyebrow, it hurt.  Yet another factor contributing to uncertainty, unlikely as it may be, is the fact that Winamp may not have actually been playing the correct frequencies.  The bottom line is that our experiments were not extremely accurate as far as the numbers go, but they still give us somewhat of an idea of what we were trying to find out.

 

Discussion:

 

            The data does not fit our original hypothesis and after doing the experiment and rehashing more of the fundamentals of sound, it does not seem like a very logical hypothesis.  The data does not prove that the optimum port length is twice the diameter of the port opening.  In fact, there is no real all-around optimum port length, at least out of the ones we measured.  Each measured port length preformed the loudest over at least a small portion of the frequencies.  However, it is seen that a port length of .0381 m, not .0762 m as we hypothesized, would be an optimum port length based on average decibel reading. 

 

            After performing our experiment, a more refined hypothesis can be formed.  If we separate the low-end frequencies, that we tested, from the high-end frequencies, we are able to determine which port length yields the highest amplitude of sound.  It would be possible to develop a hypothesis regarding the bass frequencies only.  That’s probably what we should have done in the first place if we were looking to have our hypothesis supported, but since we were attempting to explore the unknown, we were shot down by science.  Our data can be used to come to some conclusions, however.  For instance, apparently the longer the port the better, that is, if you are simply trying to amplify the bass frequencies.  It seems that if you had a three-way speaker system with an automatic crossover, you could vent the bass speaker only and raise the presence of the bass.

 

            From the final data points of each port length, we can see that they are beginning to deviate less and less.  This data can support another hypothesis that above 150 Hz, the port length no longer affects the decibel output of the speaker.  A way to improve this experiment would be to take data points from frequencies above 150 Hz and see if our educated guess holds true.  In addition, there is always the possibility of testing a wider range of port lengths. To that end, we might as well throw in the pre-experiment data that we fell upon. That is, in the original tests of the uncut, 3-foot pipe, we found that its resonant frequency was 180 Hz.  It must also be noted that the resonant frequencies of a port could play a large role in their decibel output.  Also, in order to lessen the uncertainties, the experiment could be done more accurately.  To be more accurate, the computer would need to be located outside of an anechoic room, and the decibel meter would need to be controlled remotely from outside of the room. 

 

Bibliography:

 

Kaufman, Richard  Enhanched Sound

Copyright 1988

 

Horn, Elton T   49 Easy Electronic Project for Transconductance and Norton Op Amps

Copyright 1990

 

Giancoli, Douglas C  Physics 3rd edition

Copyright 1991

 

Car Stereo Review  “VSSE Street Test Report”

October 1999  

 

S.Westenskow  “Port Types for Speaker Boxes and Subwoofers”

URL: http://xsspl.tripod.com/Audio/VentType.htm

 

Links:

 

Electrostatic Applications: Wagner - Online Electrostatic loudspeaker book order form which is a "how-to" book and an informative text on electrostatic speakers, it will provide you with step-by-step sequences for building full-range electrostatics as well as acquaint you with their basic operating principle.

 

McIntosh Loudspeaker Division - A history of the loudspeaker and has a really cool picture of a speaker combusting.

 

Khalid M. Al-Ali - Contact information for a graduate student at Cal Berkley currently involved in loudspeaker research.

 

Krix Loudspeakers - Australian Loudspeaker Manufacturer with history and product reviews to boot.

 

Ported Speaker Enclosure Design Formulas & Calculator - Self-explanatory.

 

Port Types - A list and explanation of the different types of ports for speaker boxes and subwoofers.

 

DIY Audio Projects - Just that.

 

The Perfect Speaker Box? - Opinionated challenge of the "perfect speaker box".