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Why do things get so out of control at 200Hz and higher?
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When plotting responses larger than a subwoofer standard of horizontal = 15Hz-200Hz, turn on smoothing. Smoothing is used for full range measurements (such as you are displaying), where reflections can cause comb filtering that makes it difficult to see the underlying trend of the response. It is rarely used for low frequency measurements though as it would obscure the true shape of the response and so not allow accurate correction filters to be determined.
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Why do I see output increase from about 7Hz and lower? That makes absolutely no sense to me.
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This is where your signal drops into the noise, but the meter compensation continues to raise the signal. Ignore it, it's not signal, it's noise. Limit your bottom horizontal axis to 15Hz.
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What should I have my SPL meter set at fast or slow response for C weighted?
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Slow and C-Weight.
The RadioShack meter can give a decent measure from 15Hz to 5000Hz.
Set your horizontal to that and always set your vertical to 45dB-105dB. If you want the sub only range, set the horizontal to 15Hz -200Hz. Don't use smoothing in the subwoofer range, but do so in the full range plots.
brucek