There's an article by Succi,G.P.(1986), "Flow-Generated Noise in Circular Cavities or How Teapots Whistle". Noise Control Engineering Journal, Jan./Feb. 1986, pp.8-16. It doesn't provide a quick or easy (to me) answer and it looks like you have not provided all the information needed to use it. For "screech" noise it looks like the orifice L/d ratio has to be between 0.5 and 2.0 and you need the exit flow Mach number from the equation M=v/c={[2/(gam-1)]*[1-(PT/PA)^(gam-0.5)]}^0.5 where gam =ratio of specific heats, PT=Plenum pressure, PA=Atmospheric pressure. The frequency equation is f=(c/L)*(alpha*M)/(1+alpha*M).Here c=sonic velocity, L=orifice length and alpha =??? can't find it!
Anywho, there are some results plotted for 0.5 in. diameter and 0.5 in.length orifice showing 1st stage response running from 5 to 9 KHz for Mach 0.3 to 0.7. 2nd stage is from 9-16KHz over same Mach range and 3rd stage is 13.5-20KHz from M=0.3 to 0.5. There's also an L/d =2.0 plot for d=0.5 in. showing 5 stages with disconnected response points over a 0.2-0.6 Mach range. Sounds simple enough doesn't it. If I ever find out what alpha is I'll get back to you.