A crossover frequency in a speaker system is the frequency where the woofer's output is reduced and the tweeter's output is increased.
An opamp has frequency compensation so that it does not oscillate when negative feedback is applied. The frequency compensation causes the gain to decrease starting at a very low frequency and the gain drops at 6dB per octave so that at a high frequency where the opamp has 180 degrees phase-shift then the gain is less than 1 so there is no oscillation. The datasheet of every opamp has a graph that shows how much gain is available at any frequency (bandwidth). There is also a graph of the slew rate that reduces the output level at high frequencies.
So is there always a trade off between the bandwidth and gain. So if we want a higher bandwidth then the closed loop gain will have to be less ??? what is the relation between bandwidth and stability (gain margin, phae margin) ???