If properly sealed to the window, acrylic sheets ranging from 1/4 to 3/8 of an inch thick should be enough. The important thing is to magnetically seal the acrylic sheets to the window frame. The acrylic panes are better than glass as they won't shatter if they fall.
Any Thickness Might not be Enough
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Because plastics such as acrylic do not have much mass, they are not as effective at soundproofing. Even when the acrylic is an inch thick or more, the lack of mass will prevent the acrylic from being as effective as denser materials for stopping sound.
Acrylic sheets can be somewhat effective when magnetically sealed to the window frames, but overall, they are not the best choice for soundproofing. Simple science shows that the light mass of the plastic is not the most effective soundproofing material, no matter how thick it is.