Musical Tube and String (Standing wave)

[turandorf]

Homework Statement

A brass tube of mass 20 kg and length 1.1 m is closed at one end. A wire of mass 9.6 g and length 0.4 meters is stretched near the open end of the tube. When the wire is plucked, it oscillates at its fundamental frequency. By resonance, it sets the air column in the tube oscillating at the column's fundamental frequency.

a) What is the frequency of oscillation of the air in the tube ?

b) What is the tension in the wire?

Homework Equations

Tension=(u/(time*L)) where u is the mass/length and L is the total length

The Attempt at a Solution

I know we need natural freq. but I don't know how to find it from the given data. I think the wave length is 1.1m or some fraction of that length. Any help would be appreciated.

 

[LowlyPion]

The fundamental frequency can be surmised from the length of the tube can't it?

f = v/(4L)

Since it is the same fundamental frequency of the wire, and you know the mass/unit length of the wire, ...

 

[nlightner]

I would approach this problem by first understanding the concept of standing waves and resonance. A standing wave is a type of wave pattern that occurs when a wave is confined between two boundaries, creating nodes and antinodes. Resonance, on the other hand, is the phenomenon where a system oscillates at its natural frequency when it is driven by an external force at the same frequency.

To solve this problem, we need to find the natural frequency of the air column in the tube. The natural frequency is given by the equation f = v/λ, where f is the frequency, v is the speed of sound, and λ is the wavelength. In this case, the speed of sound can be approximated to be 343 m/s, and the wavelength can be determined by the length of the tube (1.1 m) and the number of nodes and antinodes in the standing wave pattern.

Next, we can use the equation for tension in the wire (T = μL/t), where μ is the mass per unit length and L is the length of the wire, to find the tension in the wire. We can determine the mass per unit length by dividing the total mass of the wire (9.6 g) by its length (0.4 m).

Therefore, the frequency of oscillation of the air in the tube can be calculated by f = v/λ, and the tension in the wire can be calculated by T = μL/t. These calculations will give us the answers to parts a and b of the problem.

In summary, as a scientist, I would approach this problem by understanding the basic principles of standing waves and resonance and using the appropriate equations to calculate the frequency of oscillation of the air in the tube and the tension in the wire.