Finding length of tube, air column, standing waves

AI Thread Summary
To find the length of the tube, the fundamental frequency of the wire must be determined using the equation ½L √(T/µ) = f, where L is the length of the wire, T is the tension, and µ is the mass per unit length. The mass per unit length (µ) is calculated as 1.0 g/0.5 m, resulting in 0.002 kg/m. The fundamental frequency of the tube, which is closed at one end, is related to its length by the wavelength, where the length of the tube is one-fourth of the wavelength. By using the speed of sound (340 m/s) and the relationship between frequency and wavelength, the correct length of the tube can be calculated. The calculations indicate that the length of the tube should be approximately 0.85 m or 85 cm.
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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?
 
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Hint: For a tube closed at one end, how does length relate to the wavelength for the fundamental frequency?
 

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