Intuitively? Okay, think about an audio amplifier in a car. When a low bass note hits it dims the headlights. That happened because some part of the system couldn't provide the current that the bass note demanded— and he demands a lot being so long an all. He might eat up everything the capacitors have and still need more, and in the case of the car he said "You better pull the rest from somewhere because I'm coming through." So the system has to accommodate for that, making the voltage dip which will of course dim the lights. Kind of selfish, those low frequencies. You already know that more capacitance would prevent this if it's enough capacitance to accommodate, and that, as you know, is determined by reactance. That's where this ties in with your question because think about how many times you've seen headlights dim for mid frequencies (i.e. 1kHz). Doesn't happen because they're a lot easier to accommodate for (in terms of capacitance). They take what they need and GTFO real fast. So if you think about in your case, you've made accommodations for 10Hz, with 10uF he's going to be impeded quite a bit but he'll squeeze through. Meanwhile, as he's pulling the last of his 10 cycles through, 1kHz comes flying up and see's your cap as almost a short circuit so it's like "thank you I brought 99 of my friends too kbye." So you see you're passing a lot more 1k current than you are 10Hz current.

Intuitively? Okay, think about an audio amplifier in a car. When a low bass note hits it dims the headlights. That happened because some part of the system couldn't provide the current that the bass note demanded— and he demands a lot being so long an all. He might eat up everything the capacitors have and still need more, and in the case of the car he said "You better pull the rest from somewhere because I'm coming through." So the system has to accommodate for that, making the voltage dip which will of course dim the lights. Kind of selfish, those low frequencies. You already know that more capacitance would prevent this if it's enough capacitance to accommodate, and in this case, that's not so much determined by reactance but it helps you to see how low frequencies are a lot harder to accommodate for in terms of current. Think about how many times you've seen headlights dim for mid frequencies (i.e. 1kHz). It doesn't happen because they're a lot easier to accommodate for. They take what they need and GTFO real fast. So if you think about that way, then in your case that's all going to be determined by reactance. Your lowest expected frequency is 10Hz but you haven't really accommodated for him. With 10uF he's going to be impeded quite a bit but he'll squeeze through. Meanwhile, as he's pulling the last of his 10 cycles through, 1kHz comes flying up and see's your cap as almost a short circuit so it's like "thank you I brought 99 of my friends too kbye." So you see you're passing a lot more 1k current than you are 10Hz current.