I dont get it. Why is the resonant frequency 38Hz and the -3DB frequency 27Hz ? What is the difference and how is the -3DB Frequency calculated ?
The level at the resonance is not always -3dB because the properties of the resonance can vary. This is referred to as its damping level or its Q factor. A simple inductor/resistor filter gives -3dB and that's the half power point.. but a 2nd order filter can have different amounts of damping. (The speaker/box resonance is second order)
Typical sealed alignment is a 2nd order filter = 6 dB/octave roll-off and since octave spreads are exponential (1/f), - 3dB is Fl = 38/2^0.5 = 26.87 Hz
Typical BR is 4th order = 12 dB/octave, so -3 dB = 38/2^0.25 = 31.95 Hz
As Allen noted though, this is 'textbook', i.e. at a typical default alignment (box/vent) damping.
Octaves math:
Fh = Fl*2^n
Fl = Fh/2^n
n = ln[Fh/Fl]/ln[2]
where:
Fh = upper frequency
Fl = lower frequency, or the XO point in this case
n = octave spread
ln[2] = 0.6931
Typical BR is 4th order = 12 dB/octave, so -3 dB = 38/2^0.25 = 31.95 Hz
As Allen noted though, this is 'textbook', i.e. at a typical default alignment (box/vent) damping.
Octaves math:
Fh = Fl*2^n
Fl = Fh/2^n
n = ln[Fh/Fl]/ln[2]
where:
Fh = upper frequency
Fl = lower frequency, or the XO point in this case
n = octave spread
ln[2] = 0.6931
Well that would depend on what is going on at resonance. The frequency response at resonance can take on a variety of shapes. see the plot at this link for example:
The above is model of the response for a subwoofer or woofer. In the plot, the frequency, f, has been normalized by the resonance frequency, fo. There is something called the "quality factor" (abbreviated as "Q" or Q-factor) that denotes how "peaky" the resonance is. The higher the number the higher the peak is above the "passband" level before the response falls off.
Looking at the graph you can observe that for a given resonance frequency the F3 frequency can be above, the same as, or below the resonance frequency depending on the Q factor. The plot shows the frequency responses for a variety of Q values, with key of values at the bottom.
When the passband is as flat as possible before turning down into the stopband, the Q factor is 0.707 and F3=Q. When Q<0.707, F3>fo and when Q>0.707 F3<fo.
Referring to the underlined text, when the passband is as flat as possible before turning down into the stopband, the Q factor is 0.707 the –3dB point in the response is located at f/fo = 1 when using the above graph.