As you work the rope, you hands are constantly moving upwards and downwards. They are speeding up and slowing down. The power you are exerting is not constant; it changes with your speed and position. If you calculate the average power it takes to create one wave, however, it is proportional to the square of the amplitude (a) and the frequency (f). So if you move your arms twice as high OR twice as fast, you exert four times the power! Whew! That got tiring fast!