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Lately, I was watching fighter jets (F-16s and F-35s) from very close (fascinating!) and heard for the first time the "whistling noise" when they were landing and taking off. I expect it has something to do with the compressor of the fighter jets, but I am not sure because I found some sources on the Internet and they all actually say something different:

I was wondering if anyone could explain with some good sources why this "whistling noise" happens and maybe its functionality?

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Turbines have a characteristic whining sound that is most likely what you are hearing. You can hear the same effect on a turbocharged car when the turbine spools up. The sound itself isn't functional, it is simply a byproduct of the compressor working as it normally does.

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When the plane has its gear down and its flaps deployed, the airflow over the open landing gear wells and across the gear struts and whatnot can produce a distinct whistling noise that is strongly modulated by speed and angle of attack.

Even small planes like the Piper Cub "whistle while they work" and you can hear this when a Cub pilot cuts power on approach. The engine noise dies off but the whistling persists.

The most famous whistler is probably the P-51. there are many youtube videos of P-51's doing low passes and steep pull-ups at high speed, and when the AoA is just right they make a very loud and creepy-sounding whistle noise.

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