Info on soundwaves and overtones

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The discussion centers on the concept of soundwaves and overtones, specifically the first harmonic in a tube open at one end. It explains that the first resonant frequency contains only a quarter of a wave, leading to the conclusion that the wavelength is four times the length of the tube. This is due to the wave needing to complete a full cycle, which requires going up, returning, going down, and returning again. The closed end of the tube acts as a node, while the open end serves as an antinode. Understanding this relationship clarifies why the wavelength is four times the tube's length.
djef
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hallo all,

while reading some info on soundwaves and overtones I found the following statement on wikipedia:
"The first overtone is the first allowed harmonic above the fundamental frequency (F1).

In the case of a system with two different ends (as in the case of a tube open at one end), the closed end is a node and the open end is an antinode. The first resonant frequency has only a quarter of a wave in the tube. This means that the first harmonic is characterized by a wavelength four times the length of the tube."

now I want to know why it is like this:
The first resonant frequency has only a quarter of a wave in the tube. This means that the first harmonic is characterized by a wavelength four times the length of the tube.

Why the 4 ?

how do they get that?
 
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happy new year!

djef said:
The first resonant frequency has only a quarter of a wave in the tube. This means that the first harmonic is characterized by a wavelength four times the length of the tube.

Why the 4 ?

how do they get that?

Hallo djef! :wink:

The wave has to go up :rolleyes:, come back, go down :frown:, and come back, to do one wavelength.

For a tube closed at one end, the wave only has time to go up :rolleyes: …

that's 1/4 of the wavelength. :smile:
 


oh yes, indeed, thanks a lot tiny-tim
 

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