OK. Let me explain what I'm saying from a different angle. Nothing about Fourier Transform anymore
Imagine that you are in a boxing gym in front of a heavy punching bag. You have an equally strong sparring partner, standing on the opposite side of the bag.
First experiment: you push on the bag, slowly, the pressure of your hand approximating a sinusoid. The bag starts moving. Once it passes the zero velocity point on the partner's side, the partner does what you just did. Continue the exercise, both of you pushing on the bag while it is moving from you, until the bag reaches very high amplitude. That's an approximation of a normal basilar membrane resonance behavior.
Second experiment: you and your partner are punching the bag, each of you landing a strong straight every second, yet out of phase, so that the bag is hit at your side at 0 milliseconds, then at partners's side at 500 milliseconds, then at your side at 1,500 milliseconds, and so on. You can do this for a very long time, assuming you are very fit
Yet the bag will not reach the amplitude that it reached in the first experiment. That's an approximation of a basilar membrane response to an ultrasonic wave.
Third experiment: you punch the bag, once. The bag won't reach the amplitude of the first experiment. Yet if won't stay in place like it effectively did during the second experiment either. It will move, because you transferred to it mechanical momentum (mass multiplied by velocity), which was not quickly counteracted by your partner.
Eventually, the bag will settle in an oscillation with its own characteristic frequency, no matter how softly and slowly, or how hard and quickly, you punched it. The maximum amplitude it reaches will depend on the mechanical momentum transferred by your punch. You can try a "noodle slap" vs "all my body weight in" punches and observe the difference. That's an approximation of basilar membrane response to a short pulse.
In the first and second experiments, we can talk about the frequency, because the applications of force are repetitive. In the third experiment, we can't, because with just one punch, how do we determine the time period until the second punch? The second punch simply doesn't come during the third experiment.
Analogously, the basilar membrane effectively ignores a vigorous application of ultrasonic force analogous to the second experiment. Yet it has to react, somehow, upon getting half of that ultrasonic wave in the third experiment, because the half wave is asymmetrical, and thus transfers mechanical momentum.