Flow-induced aeroacoustic noise is often caused by the laminar flow on the surfaces shedding off of the back surface and exciting the air causing noise (vortex shedding). What is usually done is to install something in the upstream flow to break up the laminar flow so that a turbulent flow exits off of the back surface. This will eliminate in-phase vortex shedding and eliminate the flow-induced noise.
Generally speaking, sound waves cannot pass through a "rigid" object. If sound is generated within an acoustic volume, it will excite the surrounding structure and the surrounding structure will radiate sound to the outside. Usually, when the frequency of the acoustic volume matches a structural panel frequency, you will get amplification of the sound to the outside. It is generally difficult to just stiffen the structure to eliminate the noise, as the noise still has energy and this energy will excite other parts of the structure.
For your problem, I am guessing that as you change the position of the slide, you are exposing the surrounding structure to more or less aero-acoustic excitation. If you want to eliminate sound amplification off of the body of the slide, you will need to perform a modal analysis to find out what frequency the body is vibrating at various positions of the slide. You can then stiffen the body (to move the resonance frequency out of the range of the aero-acoustic noise), or you can apply a viscoelastic damping treatment on the body (to dampen the structural vibration and attenuate the structure-radiated noise), or you can put a sound dampener on the body (to absorb the structure-radiated noise). Alternative (non-active) approaches would involve eliminating or attenuating the aero-acoustic noise altogether by changing the flow rate of the fluid in your system or placing a turbulent flow generator upstream of the slide to eliminate in-phase vortex shedding.
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