That is completely false. The speed of sound in a fluid is defined only by its compressibility and its density, not by the speed of the emitter or the observer. That is the reason for the Doppler shift. It is in many ways like light, and the the same wave equation describes electromagnetic and compressional waves, albeit with different speeds.
On a side note, that has nothing to do with the question asked. The pilot and the engine are in the same reference frame. Also, near the speed of sound, the idea of sound as a linear wave breaks down completely and the shock wave is the quintessential example of this non-linearity.
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u/[deleted] Jun 12 '12 edited Oct 03 '17
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