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

Sagot :

Answer:

[tex]25\%[/tex] of the wavelength is between resonances in a closed end tube.

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

[tex]f=\frac{L}{\lambda}\times100\%........................(1)[/tex]

Here, [tex]f[/tex] is the required percentage, [tex]L[/tex] is the length of the tube and [tex]\lambda[/tex] is the wavelength of the standing wave.

Substitute [tex]\frac{\lambda}{4}[/tex] for [tex]L[/tex] into equation (1) o calculate the required percentage.

[tex]f=\dfrac{\frac{\lambda}{4}}{\lambda}\times100\%\\~~~=25\%[/tex]