Turning on LED when input voltage has desired frequency.
Use a voltage to frequency converter - it will produce a dc output voltage that is proportional to frequency. Try the LM(C)567: -



Then use a "window" comparator to "accept" voltages between the appropriate two limits that correspond to 950Hz and 1050Hz. The LM(C)567 effectively does this by using a phase-locked-loop and phase and amplitude detectors, in effect it is a synchronous detector.