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    Comparison Responses

    This is a little lengthy, but bare with me. It was created upon request. The information here is for informational purposes only and does not contain much about helping with design, as those parts were intentionally left out for now. The response information here was measured and calculated in a much quicker manner than usual and maintains a sense of realism and honesty. Please enjoy.


    This is an introduction to the basic form I use to figure an accurate response based on the added gain of the vehicles transfer function. This is only for my personal vehicle, and the cabin gain shown will not be reflected by an average, nor does it relate to any other vehicle on the market. Most designers who do inhabit cabin gain, use very generic forms of averaged dB increases per octave of somewhere between 6-12dB.
    This will show you the accuracy of my design process and hopefully conclude the theory/practice misconception that hovers over the audio community based on inaccurate design approaches, that have damaged the trust of a proper calculation in this world in comparison to real world response.
    I am going to be using a generic 6.5” driver with an Fs of around 57-62Hz, depending on the applied voltage, related to impedance changes.

    Information will be added each post due to the length of the project.





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    Re: Comparison Responses

    Here are the basic parameters I have calculated so far:


    Uploaded with ImageShack.us



    This does not include the Mechanical mass as the Vas has to still be calculated. This will be done after the test box is completed.
    So, in order for this project to be complete accurately, many programs and hand calculations will be done that will not be shown, due to the amount of work I have put together for years to get the information I need for a response. This will remain classified, with the exception of using hornresp to verify my response, NOT for creating the response. I do not like ot use hornresp to do the work for me. I use other calculations for figuring proper compression and port/path dimensions and areas using the drivers parameters and other known variables needed to figure for those parameters of the enclosure as a basis. This is important in getting the accuracy I put my name on.

    So, let’s get started! First, we have a driver figured. Now, we have to construct a test box that is the optimal volume for the drivers acoustical compression to be calculated. We will figure for a box that is just a bit larger than the drivers outer dimensions. This will give us a volume of 7.75”x8.75”x7.25” or around 0.285 cubic ft. The reason for this size enclosure is that if made too large, inaccuracies occur when calculating Vas, and if made too small, the resonance will change to dramatically due to impedance rise to figure an accurate Vas. This size will work fine. The driver will be placed outside of the enclosure as no terminal connections within the enclosure will be used or needed. We will also at the cutout volume of the driver within the thickness of the wood as volume as well. This is calculated as a cutout diameter of 5.75” and a wood thickness of .75”. This has to be converted to a cylindrical volume, so diameter will be converted to radius and using the formula: Pi*(rad)^2 we can figure for square area, then multiply by the wood thickness for volume.
    So, the radius will be 2.875. That *2 is 8.265625. Multiply that by Pi, and you get a square area of 25.954 square inches or 167.45 square cm, by multiplying square inches by 6.4516. So, volume will be 167.45(.75*2.54)=318.9923 cubic cm. This will be added to the 0.285 cubic ft volume. But we first need to convert 0.285 cubic ft to cubic cm. This is done by reverting back to the actual dimensions (7.75, 8.75, 7.25). If you multiply them to get cubic in, it can then be multiplied by 16.387064 to get cubic cm. This will give you 8056.55 cubic cm. So, 8056.55+318.9923=8375.5423 or 0.2958 cubic ft.
    Note: Cm are used for higher accuracy.





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    Re: Comparison Responses

    So, now we have the volume of the enclosure figured. Now we have to construct it. Here, I have attached some pics of the build:









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    Re: Comparison Responses

    So, now that we have a test box, we can mount the driver and get ready for calculating acoustical compression volume. Why is it important that we need this value? Well, without it, many calculations cannot be made, but the most important real-life reason, is without knowing the 1:1 compression ratio of the driver, will cannot conclude a proper compression volume without having to build the box over and over and test over and over, like many do for SPL competitions to figure for greatest SPL output. This is mainly to show that this can be done WITHOUT all the fine tuning being the major factor in the response, and allowing calculations to become so accurate, that we should be able to get to a point where only a single box needs to be made, without adjustable ports, or any of that extra hands-on stuff that so many rely one. This is not to say that it is inaccurate to do all that extra work, but it can be avoided by getting rid of the misconception that calculations just are not enough for accuracy. That is the main purpose of this project.

    So, though many will argue this, accuracy of the calculations I use have been down to a few inches of measurements for resonance points, and down to a few Hz of accuracy for SPL output. This will be proven effective here.

    Moving on………..





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    Re: Comparison Responses

    So, figuring for accurate response…. How do we start? Well, first, it would be good to know the vehciles response information to be configured with the anechonic response of the enclosure. This way, when loaded, the proper resonances will be excited for an added gain to get more of what you will hear from a specific listening position, or for an average of the entire vehicle. For this, we will figure for the headrest position and the mic position as well, for stock SPL competition.
    First thing to know is the vehicle dimensions, in inches, not feet as this will be more accurate.
    So, for my vehicle, dimensions are: 110”Deep, 62” wide, and 48” high. This will be used to calculate the vehicle response curve. This part I will not show you as it will take a while and I simply do not want to reveal my personal findings, but here is the final responses after all of the calculations(this took a few solid hours straight to complete).


    Uploaded with ImageShack.us





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    Re: Comparison Responses



    Uploaded with ImageShack.us

    The second one is the mic position
    From this response, you can see that I have an excited resonance around the 62Hz range. And if you figure the simple calculation (used by many others), you will see that by calculating for 110” at half-wave (not quarterwave…that is not what I use), then you get 110/12=9.1667ft, then 1127/9.1667 which is 122.95Hz, and at half wave its 61.47Hz! Pretty darn close I would say.
    Now, since we are now aware of the peak resonance of the vehicle, and that it so happens to match with the basic waveform calculation so popularly used, there is a few more things to consider. One of those is, will 62Hz be good to use for a burp? Well, this is a part of my job that requires quite a bit of explanation, as most would take 62Hz as “easy spl”. But there is a reason for this. This frequency does not have to be the frequency of choice. And most would consider exactly half of this as a base frequency. This is where again, I differ in my calculations. I would agree that quarterwave resonance is great for spl configuration, but not for direct spl output, more so, as a guide to a complete response passband at LF cutoff. For instance, the way that I figure for accurate response curves in different vehicles, does reside around QWLF cutoff, as it physically makes sense to do so when considering efficiency in the design. But this will be shown as well. Right now, I would like to concentrate on direct spl configuration, as this will accurately show the basis of my project goal---to show that theory can be as accurate as practice.





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    Re: Comparison Responses

    So, here is where I consider two different frequencies in regard to two different spl listening positions. The reason for this is obvious…….two different length of paths the sound waves travel, hence different frequency resonances. So first, we figured the resonance using my calculations and bounced them off of what most designers do and found them to be identical……at least to the nearest whole number. This will say a lot about my accuracy as well. Now, this was for direct mic position at 110” from the rear driver location and also from another position important in gain resonance…….the angle from the back window directed straight at the mic. This position will have the same distance in my vehicle as the driver position, so only one of those will be used.
    Now, we have to figure for headrest position. Again, my way is different and I come up with a resonance of about 48Hz. Now, if you look at the headrest response, you will notice that there is not a 48Hz peak shown. There are acoustical reasons for this. Here is a modified length to 48Hz halfwave resonance that you can verify by the circled peak at full wave resonance at around 100hz.


    Uploaded with ImageShack.us
    But you will notice, the 48Hz does not show up still. This is where a lot of people are tricked into hearing resonances that do not show on the graph, and as I believe, is the main reason why people will say, theory does not equal practice. I will try to verify this when the build is complete and we can test a resonance, as the enclosure will be sealed for direct front wave response with no phase problems from the design, only from the vehicle, as this is what we are concentrating on.





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    Re: Comparison Responses

    So, here is the box completed. Simple, no sanding needed, just sealed.



    Uploaded with ImageShack.us
    Now, since we have a test box, I have calculated the Vas to be 5.0857 liters. Now, I can figure for mechanical parameters.





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    Re: Comparison Responses

    So, this is done. I have a box response here:


    Uploaded with ImageShack.us
    Now, I will use an FFT analyzer to measure a real response. I will be placing the driver 1 meter from the source, it a virtually anechonic environment, due to the output voltage being less than 1V. This allows for minimal, if any, resonances due to timing loss in a room that is 9ft high, 14 ft wide, and 19 ft long. With less than a volt of output, this is not a problem on the measured response at 1meter.





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    Re: Comparison Responses

    After the measurement, here is what I put together for a comparison response with the calculated one:


    Uploaded with ImageShack.us
    The white response that extends to 15hz is the calculated one. The purple response is the non-smoothed response, and the turquoise response is the 3rd octave smoothed response(accounting for resonance).


    You see how the measured responses follow the calculated one quite well. This is a sealed design, so if this didn’t match, I would quit designing all together, lol.
    Now, there is a noticeable dip around 60Hz, which seems to actually be room resonance as the room calculated response is this:


    Uploaded with ImageShack.us

    This is with the mic and the box positions configured correctly in the room.
    Also, we can correspond the 35hz rise, 85hz rise and the 110hz rise.





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    Re: Comparison Responses

    So, since Im working with realtime, this will have to be considered. But the response is still pretty close to calculated even with the huge dip in the room. But this is a good point that the room response is nearly dead on. This is a great way to conclude the project already, but we will go further with a full response IN the vehicle as well.

    Ok, so now that we know the response is accurate, we can use it to calculate the transfer function of the vehicle into it.
    Here is what I came up with for a vehicle response:



    Uploaded with ImageShack.us
    This is the final mic response



    Uploaded with ImageShack.us
    This is the final headrest response
    They look fairly identical, but this is mainly due to the smoothness of the anechonic response, which allows cabin gain to take full control over the response curve. But you notice that, like other sealed designs, the flatness occurs quite well in the passband of this driver.





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    Re: Comparison Responses

    So, as far as the vehicle response, what I have calculated to be a great one to use, aside from this particular project, has been calculated at 31-124Hz due to the size and dimensions of my cabin. This is one of the reasons I chose this vehicle, due to the passband it will allow with respect to most music. If you take a truck for instance, you will see higher resonances in the truck if its dimensions are smaller. Take a truck with a 6ft length. This will allow for an optimal response passband of 47-188Hz, which will cause much higher gain below 47Hz. I do not like this effect as I tend to enjoy smooth accurate bass rather than peaks. So, having my cabin structure will actually prove quite challenging in an spl setup for this small driver….not optimal at all, but this is just a project of informational reasons.

    Next, I will be taking the enclosure into the vehicle for some testing and comparison of the calculated response. It has to be mentioned, that I need to also figure for equalization at the LF cutoff of the amplifier and slope of the LF response as it will likely show that the 20Hz dB level may be lower than calculated for now. This will be accounted for in the process if needed. It will also be noted that the actual dB levels will not be the same due to the calculations being strictly informational for the comparison, because the calculated response is measured at 2.83V. it may be figured for my output in the vehicle to be at 2.83V as well for higher accuracy of dB readings. This, as well, will be accounted for as this is an SPL example and exact dB levels are extremely important.





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    Re: Comparison Responses

    Update: While I was waiting to go to work today, I wanted to further test the resonance I have calculated of the vehicle using another form of propagation effect.

    Now, I had made a simple Bass reflex design for a couple of DUAL 12s that I use for testing purposes. I extracted their parameters, and used the ever popular hornresp to verify my response information. For an anechonic response. Here is the anechonic response:



    Uploaded with ImageShack.us
    Now, you may be wondering if you can calculate for gain in hornresp. Next, is a gained response I used in hornresp to calculate this response into my vehicle gain. Now, if you remember, from my transfer function calculations, I have figured for a gain at halfwave of 62Hz, and verified that with the simple formula for length of a wave. Again, longest distance 110”. 110/12=9.1667. 1127/9.1667=122.95. 122.95/2(for half wave propagation) =61.47Hz.





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    Re: Comparison Responses

    So, figuring for the added model of my vehicle, and treating it as enclosure volume (as it really should be anyhow.maybe more on this later or another topic). And I get this:

    Uploaded with ImageShack.us


    This verifies, in theory, the gain at 62Hz! Now, listening position will alter this respons quite a bit if measured from other than windshield position, but this is just a calculated example of the power of half wave resonance vs quarterwave resonance, in my perspective. For this, most of my designs are revolved around that for a passband. For instance, and vehicle with lowest room mode of a length of 6ft, will give you a half wave resonance of 93.92Hz. This is where most of the efficiency will revolve around. And the LF would be the quarter wave resonance of 47Hz. And the full passband for this vehicle would be optimal from 47Hz- the fullwave of 187.83Hz or 189Hz. So, from 47Hz-189Hz, is the optimal response passband for this type of vehicle. This will allow any resonance below 93.92Hz to have gain, rather than 40-60Hz, which will actually decrease efficiency! That is one of my tricks that works well. And this does not mean it will play only to 47Hz. It just means for efficiency and optimum range. Below 47Hz should be great output in that sense as well with the gain of the vehicle taken into consideration. This will change the LF output of the graph, but the gain will be at the same positions if calculated as this one was.
    Here is the design idea used to figure the gain using hornresp:


    Uploaded with ImageShack.us

    ---------- Post added at 12:07 PM ---------- Previous post was at 12:07 PM ----------

    In this design, the trunk space was utilized as compression area, as that is exactly what it is anyhow, with dampening anyhow, but figured for full resonance affects.
    Now, for phase, in hornresp, at the nominal frequency of 77Hz, which is the middle of the passband for a broad average of explaination, it shows it at 156.3 degrees. Also, the 62Hz peak involves the full cabin, and this shows just the rear as it was needed for me to figure for volume correctly, but the front is not as oblique, so not needed to sketch it out. This is just having the rest of the vehicles remaining cabin, but to include that if I were to make walls behind the c pillar, that it would not change the resonances, but will excite them, and hornresp can show that as well, by figuring for the vehicle as part of the design. I will be experimenting with this in the future, I just came across this and verified it with this design. It may prove to be incorrect further down the road, but for now, maybe something can come out of it, I don’t know yet, but the calculations are completely verified here anyhow.


    Uploaded with ImageShack.us
    It should reside around more towards 180degrees, but hornresp does not taken into major consideration the angle rather it uses expansion rate than directivity of the throat to mouth area (one of the reasons I do not do my full calculations with hornresp, and use it more merely recognition and verification).

    ---------- Post added at 12:08 PM ---------- Previous post was at 12:07 PM ----------

    So, this means that the direct off axis response of this design is fairly close to accurate with the phase and with the adjustments needed in the calculations without hornresp, this will be precise. But this was mainly to show the correlation of my gain response to calculated response of another program than what I use, which further verifies its accuracy, even when the angle of the back window is not fully taken into consideration…..the resonance is still accurate due to dimensions being close and volume being exact. So, the leniency of a design can be given to angle for some degree, which is why taking the seats and the windows into the full response is not really necessary, more so can be averaged for the transfer function to be accurate( and likely why no one considers obstacles in the vehicle as affecting the response, due to the resonances over time being filled into the environment as long as RT60 is overlapped continuously.





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    Re: Comparison Responses

    So, back to the actual measurement of the original concept:
    Ok, so here is what I have for you with the test box and sub located in the calculated area and the mic in the mic position.


    Uploaded with ImageShack.us

    Placement from front or rear of the mic was not important as it deals with the reflective waves from the windshield. Non-directive was purposely done.


    Uploaded with ImageShack.us


    Uploaded with ImageShack.us
    Sub placement shown here, and the calculated replacement was Identical, corner loading at about 10” from the floor and 12” from the right.





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