Can you make a circuit where a microphone listens to a beat (the bass in a song) and then blinks a light in response to that?
Of course, but I fail to see the connection with robotics ??
Back in the seventies, we called such circuitry "Light Organs" and the better of them was made with filtering into 3 or 4 frequency bands.
A 4 pole low pass filter should suffice '(perhaps even 2 poles might do) or an elliptic filter (made with L's and C's) using an f3dB
of say 300Hz to 600Hz - you could make FFT analysis of some typical rave music to find the optimum frequency to use.
Clapping and loud/sharp noises at higher frequencies would set it off as well - analog filters cannot be made as brick wall steep as digital filters, but a DSP would be serious overkill for this.
The scenario would be in a nightclub/rave/anywhere with loud music, would it work? Or would there be too much background noise, and the microphone would be confused and not pick up the beat.
I have never been to a rave, but I have an impression, that it's more or less people on E, Pogo'ing to electro-music, instead people on W(hiskey) to Rock'N'Roll - so I assume the signal/noise ratio won't be all that different - perhaps better (except for your ears), given the last few decades of amp and speaker development though.
The project I'm thinking of is techno gloves that flash lights to the beat of the music.
You could up that with a string of LEDs each finger and let the light flash out along the fingers (with a slower retract) - something like an LM3915.
This could even be made in a controller, triggered by the output from the preamp/filter - and if you wanna go nuts, use RGB LEDs - colors could fade and blend - expanding and retracting, or color could be determined by the rhythm (the b.p.s.), the overall frequency components of the music, or whatever you can imagine.
Plan B is put a potentiometer on them so you can adjust the speed of the blinking to the beat of the music.
Bad idea IMO, but could be realized with a controller as well - hold a button for eg. 2 seconds (to enter "learn mode") and then tap it twice to the beat. Then it knows the interval (until the next piece of music - but... I'm not sure the girls will find it all that attracting, that you have to reprogram your gloves at each new piece of music - and let's face it... The girls are the reason that we go to such places