Yes, at a rate determined by the slope of the filter...ie 6dB, 12dB, 18dB, 24dB The bigger the number, the more extreme the cut.
For instance, 40Hz is one octave below 80Hz. Thus, on a 6dB per octave slope, it would be 6dB lower. 20 Hz would be 12dB lower
On a 12dB per octave slope, 40Hz would be 12dB lower, but 20Hz would be 24dB lower!
60Hz would be down about 3dB with a filter set at 80Hz with a 6dB per octave slope. There IS the taper of the filter too, which may or may not be linear. I believe they generally are.