Finding the Length of a Resonating Air Column

[soulja101]

Homework Statement

What is the shortest air column, closed at one end, that will resonate at a frequency of 440Hz, when the speed of sound of 352m/s

Homework Equations

the patterns

The Attempt at a Solution

ive tried

 

[AlephZero]

See your other post - the same hints apply.

 

[kyle8921]

using the formula wavelength = 4L/n, where L is the length of the air column and n is the harmonic number. However, this formula assumes that the air column is open at both ends. To find the shortest closed air column that will resonate at 440Hz, we need to modify the formula to account for the closed end.

One possible solution is to use the formula wavelength = 4L/(2n+1), where L is the length of the air column and n is the harmonic number. This formula takes into account the closed end of the air column and will give us the shortest length that will resonate at 440Hz.

Another approach could be to use the formula frequency = nv/4L, where v is the speed of sound. In this case, we can rearrange the formula to solve for L, giving us L = nv/4f. Plugging in the values, we get L = (1)(352m/s)/(4*440Hz) = 0.2m. This would be the shortest closed air column that will resonate at 440Hz.

It's important to note that these calculations assume ideal conditions and do not take into account factors such as air temperature, humidity, and the shape/material of the air column. In a real-life scenario, these factors could affect the actual length of the resonating air column.