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?

 

[m2003]

I would first suggest double-checking your calculations and making sure you are using the correct units for all values. It is important to maintain consistency in units when solving equations.

In addition, it may be helpful to draw a diagram or visual representation of the problem to better understand the variables involved. This can also help to identify any potential errors in your calculations.

Another important factor to consider is the density of air inside the tube. This information is not provided in the given problem, but it is necessary to accurately calculate the length of the tube using the given equation. You may need to do some research or make an assumption about the density of air in order to find an accurate solution.

Overall, it is important to carefully review the problem and all given information, use the correct equations and units, and consider any potential factors that may affect the solution. If you are still having trouble, I suggest seeking assistance from a classmate or your instructor.