Question

What fraction of a wavelength of a standing wave pattern is between resonances in a closed end tube?

Answer 1

`25\%` of the wavelength is between resonances in a closed end tube.

Step-by-step explanation:

In an one end closed tube, the fundamental resonance occurs when a node is created at the closed end and an antinode is created in the open end.

Thus, for fundamental resonance, the entire length of the tube encloses one-fourth of the wavelength of the standing wave.

The formula to calculate the percentage of the wavelength in a closed end tube is given by

`f=(L)/(\lambda)*100\%........................(1)`

Here,
`f` is the required percentage,
`L` is the length of the tube and
`\lambda` is the wavelength of the standing wave.

Substitute
`(\lambda)/(4)` for
`L` into equation (1) o calculate the required percentage.

`f=((\lambda)/(4))/(\lambda)*100\%\\~~~=25\%`