Finding length of tube, air column, standing waves

[aliaze1]

Homework Statement

A 50-cm-long wire with a mass of 1.0 g and a tension of 440 N passes across the open end of an open-closed tube of air. The wire, which is fixed at both ends, is bowed at the center so as to vibrate at its fundamental frequency and generate a sound wave. Then the tube length is adjusted until the fundamental frequency of the tube is heard. What is the length of the tube?

Speed of sound is 340 m/s

Homework Equations

½L √(T/µ) = f
Vsound = 340 m/s

The Attempt at a Solution

I keep getting 0.362m or 36.2 cm but it is incorrect..any help?

 

[Doc Al]

Show your work step by step.

Hint: For a tube closed at one end, how does length relate to the wavelength for the fundamental frequency?