Why does takeoff in a commercial jet sound like tuning a guitar?

Answer 1

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When you can hear that slightly wavering sound the engines are not operating at exactly the same RPM, so they do not produce the same audible frequencies. Therefore you hear the oscillating sound like two guitar strings slightly out of tune. It usually only happen at takeoff power. When power is reduced for normal climb and cruise the rpm's are matched. 

Answer 2

To me, the high bypass turbofans used in modern commercial jets tend to sound like a buzz saw.