Lightweight audio listener for detecting blip
One lighter-weight approach might be to use a narrow-band IIR filter centered at your blip frequency, rectify or square, feed this result to a low-pass filter, and look for a value passing some threshold.  A Goertzel filter is another possibility.

Note that the most current iOS Accelerate framework includes a reportedly power-efficient biquad IIR filtering function.  Also note that on recent iOS devices, even a more heavyweight approach (FFTs, autocorrelation, and such) on a single channel of real-time audio input might use only a tiny percentage of total device power.