There are several MAJOR issues/challenges and you might want to consider something other than the Arduino…
This echo device will work like
The Arduino doesn’t have enough built-in memory for any significant delay. i.e CDs use a sample rate of 44,100 samples per second. At 16-bits, it takes 88,200 bytes to store 1 second of mono sound. (You wouldn’t need such a high sample rate for bass-only, but that’s the idea.)
The Arduino’s ADC is only 10 bits, which may or may not be enough depending on what kind of quality/fidelity you need.
- sense sound with microphone
Do you have a microphone board/circuit? A microphone plugged directly into the Arduino won’t have enough signal, and the signal has to be biased for the Arduino’s ADC which cannot accept the negative half of an AC signal.
- choose low frequency sound (20 Hz ~ 100 Hz) from the original sound
If you don’t need a sharp filter, you can use a simple RC filter (a resistor & capacitor). You can build a more advanced filter with an op-amp, or it can be done digitally.
- echo(emit) the low frequency sound through woofer (about 200W, 8ohm)
The Arduiono doesn’t have a DAC (digital-to-analog converter). I has 8-bit PWM which can approximate analog, but you’re not going to get good quality. (And, you’d probably have to increase the PWM frequency from the default.)
- which amplifier is suitable for woofer
That’s the EASY part! How big is your woofer and how loud do you want to go? Something like [u]this[/u] would work, depending on how loud you want to go. Subwoofers made for home theater systems are usually “active” with the amplifier built-in. Computer speakers are active too, so a compute speaker with a subwoofer would work.