An acoustic filter is to be designed to attenuate sharp pressure transients in air above $50$

Hz$.$ The volume of air contained in the pressure$-$transducer cavity is $0\mathrm{.}6$ in$3,$ and a

capillary tube connects the cavity to the pressure source. If the $50-$Hz frequency is to be

attenuated by $50$ percent, determine the capillary length and diameter for system natural

frequencies of $($a$)50$ Hz$,($b$)100$ Hz$,$ and $($c$)500$ Hz$.$