This is a very nice explication, but it is also perhaps worth noting that the built-in AudioDelay function can be used to implement Karplus-Strong synthesis (this is one of the "Neat Examples"). For example:

freq = 60;
feedback = 0.99;


AudioDelay[
    AudioGenerator["Pink", .01], 1/freq, feedback, 
    PaddingSize -> 5] (* padding runs the audio longer than the brief initial impulse *)

(* another version with a low-pass cutoff filter *)    
AudioDelay[
    AudioGenerator["Pink", .01], 1/freq, feedback, 
    PaddingSize -> 5, Method -> {"LowpassCutoff" -> Quantity[8000, "Hertz"]}]