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

[mohit.choudha]

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

 

[berkeman]

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?

 

[tomcue]

for your question. To solve for the frequency of oscillation of the air column, we can use the formula f = nv/4L, where n is the harmonic number (in this case, n=1 for the fundamental mode), v is the speed of sound in air (approximately 343 m/s at room temperature), and L is the length of the tube (1 meter). Plugging in these values, we get a frequency of approximately 85.75 Hz.

To solve for the tension in the wire, we can use the formula T = (mL^2f^2)/4, where T is the tension in the wire, m is the mass of the wire (0.010 kg), L is the length of the wire (0.30 meters), and f is the frequency we just calculated (85.75 Hz). Plugging in these values, we get a tension of approximately 7.33 N.

It is important to note that these calculations assume ideal conditions and do not take into account any external factors that may affect the frequency of oscillation, such as air resistance or the stiffness of the wire. Additional measurements and adjustments may be necessary for a more accurate result.