You have designed a new musical instrument of very simple construction. Your design consists of a metal tube with length L and diameter L/10. You have stretched a string of mass per unit length \mu across the open end of the tube. The other end of the tube is closed. To produce the musical effect you're looking for, you want the frequency of the third-harmonic standing wave on the string to be the same as the fundamental frequency for sound waves in the air column in the tube. The speed of sound waves in this air column is v_s.
What must be the tension of the string to produce the desired effect?