This question already has an answer here:
I had a flight yesterday on an AA Embraer ERJ-190. As the plane idled at the end of the runway there was the familiar high-pitched jet whistle, which increased in pitch as the engine started spinning up. But, when it reached full power, the whistle was joined by a far-lower-pitched metallic whine, which persisted until the pilot throttled down after the initial steep climb.
I've heard this before on some (but not all?) planes. By ear, the whistle was about four an a half octaves above the whine, which is about a factor of 24 (I may have been off by an octave, or another factor of two).
On a past flight I calculated that if the main fan spun so that its outer edge was moving at the speed of sound, the whine would be at about the rotational frequency of the fan. If the fan had 24 blades (or 48 if I have the wrong octave) then the whistle could be the fan blades, and the whine the fan itself.
One explanation could be that there's something asymmetrical about the fan, e.g. one blade is a bit too long and hits the housing when at full power. (Of course, this would make no sense from an engineering and reliability standpoint.)
What causes that far-lower-pitched metallic whine?
Edit: I just returned on a JetBlue flight, but also using an ERJ-190. Where before I was seated in row three, this time I was in row 24 of 25. On takeoff, there was only a loud roar; no "whine" or "whistle". So, it's pretty clear that the noises I'm referring to above are emitted from the engine intake.
And, on this page I found a photo of the ERJ-190's GE CF34-10E Efficient Engine's inlet:
Sure enough, the intake fan has 24 blades. So, my above guess on the frequency ratio between my "whine" and "whistle" has some physical basis.
And, I'd like to respond to a comment by @kevin:
Could it be that the "whine" always exists in the frequency spectrum, but it's just below our human ear detection threshold (both pitch and amplitude) during low rpm operation?
When the "whine" starts and ends, my impression is that yes, the pitch rises as it initially strengthens, and falls as it finally fails. However, its volume is strongly pitch-dependent, so that it is far quieter when running at 80% of the maximum pitch/RPM, and inaudible below that. It sounds as if that blade which purportedly hits the housing only does so above a certain RPM (again: this is what it sounds like, it almost certainly is not what is actually happening). More generally, my interpretation is that the cause of the "whine" only happens above a certain RPM.
Edit 2: @fooot was kind enough to point out another question that is basically a duplicate. My text and suppositions are (I think) a lot clearer, but the other question links to two videos that demonstrate exactly what I've been talking about:
Neither of the answers to the other question are correct; one focuses on the fan blade noise (too high-pitched) and the other on pressure equalization vents (not engine-speed related).