Usually speakers do not have a high-pass filter to cut off low frequencies, for two reasons: 1) The inductor coils and capacitors required to work at such low frequencies are very large and expensive. 2) Any AV receiver, and some stereo receivers have built-in bass handling features that allow you to do this digitally, without the need for those large & expensive analog filters.
Most woofers naturally roll off their response below a certain frequency. It depends on the driver and the cabinet. Parts Express suggested sealed and vented cabinets for the DC-250 10" woofer:
Sealed Cabinet – volume 1.39 ft³, with an F3 = 55 Hz
Vented Cabinet – volume 4.47 ft³, with an F3 = 29 Hz
The F3 frequency is that frequency where the driver's sound pressure level (SPL) is 3 dB lower than the driver's rated SPL of 88 dB. It's commonly accepted that a change of ±3 dB is about the smallest interval most people can detect. (That topic can be debated, but let's not worry about that now.) Below the F3, the driver's response will naturally decrease, falling off at 6 dB/octave for a sealed cabinet, and 12 dB/octave for a vented cabinet. You have to decide what size cabinet you want to build, and what bass performance you want. (Hint: 4.47 ft³ is a rather large cabinet.)
That's not quite correct. Drivers do a poor job producing
off-axis sound at wavelengths shorter than the driver's diameter. And that's only a rough rule of thumb. It really should be measured while the driver is mounted in a cabinet with dimensions you intend to use.
Parts Express publishes this frequency response curve for the DC-250. The black curve is when the measuring microphone is on-axis (0° off-axis), red is 15° off-axis, green is 30°, and blue is 45°. Above roughly 1.5 kHz, the green line is about 3 dB below the black line. Above that frequency, this driver's off-axis response falls significantly. That will result in poorly dispersed sound, a poor sounding speaker. The solution is to cross this driver well below that frequency. Moreover, above roughly 2 kHz, this woofer is in break-up mode. Make sure to avoid that by crossing over by at least 1 octave lower if you use 4th order crossover slopes, and 2 octaves lower with 2nd order slopes.
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I really don't think a 10" woofer can make a good sounding 2-way speaker. It's meant to be used in a 3-way design.
I'd suggest a 6½" driver if you plan on a 2-way speaker, with that Dayton DC-28FS tweeter. Another rough rule-of-thumb is to use 3× the tweeter's resonance frequency (Fs) of 905 Hz as a minimum crossover frequency for a 2nd order crossover, and 2×Fs for a 4th order crossover. That becomes 1800 to 2700 Hz. Crossing a tweeter too low will lead to audible distortion, or even tweeter failure. As usual, spending more money on a tweeter can get you better low frequency performance.
Shielding the speaker motor's magnet prevented interference if they were too close to an old TV with a cathode ray picture tube. Modern flat screen TVs don't require shielded speakers.