How Do You Calculate the Frequency of Oscillation for a Resonating Air Column?

AI Thread Summary
To calculate the frequency of oscillation for a resonating air column in a closed tube, the fundamental frequency can be determined using the formula f = v/4L, where v is the speed of sound in air and L is the length of the tube. For a 1-meter-long tube, this results in a specific frequency based on the speed of sound, typically around 343 m/s. Additionally, the tension in the wire can be calculated using the relationship between tension, mass density, and frequency of the vibrating string, typically represented by the formula T = 4Lf^2μ, where μ is the mass per unit length of the wire. The discussion emphasizes the need for participants to demonstrate their problem-solving efforts to receive guidance. Understanding these principles is essential for accurately solving the problem presented.
mohit.choudha
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Do not know how to solve this:

A tube 1 meter long is closed at one end. A stretched wire is placed near the open end. The wire is 0.30 meter long and has a mass of 0.010 kg. It is held fixed at both ends and vibrates in its fundamental mode. It sets the air column in the tube into vibration at its fundamental frequency by resonance. Find:
a) the frequency of oscillation of the air column
b) the tension in the wire.


Thank you
 
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mohit.choudha said:
Do not know how to solve this:

A tube 1 meter long is closed at one end. A stretched wire is placed near the open end. The wire is 0.30 meter long and has a mass of 0.010 kg. It is held fixed at both ends and vibrates in its fundamental mode. It sets the air column in the tube into vibration at its fundamental frequency by resonance. Find:
a) the frequency of oscillation of the air column
b) the tension in the wire.


Thank you

Welcome to the PF. Per the Rules link at the top of the page, you need to show some effort on your problem, in order for us to provide you some tutorial help.

What is the fundamental resonance of a tube like that? What is the relationship between a string's tension, mass density, and resonant frequency?
 
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