Width of Pipe and Frequency of Resonance Waves

[manohman]

In the Berkley Review it says that "Width of the pipe has no impact on the frequency of resonance waves".

Just trying to understand why?

Frequency = nv/2L for an open tube or standing wave.

But if the width of the pipe is smaller, then wouldnt the density of the particles increase? (Smaller volume, same number of particles/mass).

and the speed of a sound wave is inversely proportional to the density of the gas particles. v = root (vP/density)


What am i missing here?

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[justadream]

@manohman

Why are you thinking about density of particles?

What particles are you referring to? The light? Just think of it as a wave.

 

[The Brown Knight]

In the Berkley Review it says that "Width of the pipe has no impact on the frequency of resonance waves".

Just trying to understand why?

Frequency = nv/2L for an open tube or standing wave.

But if the width of the pipe is smaller, then wouldnt the density of the particles increase? (Smaller volume, same number of particles/mass).

and the speed of a sound wave is inversely proportional to the density of the gas particles. v = root (vP/density)


What am i missing here?

Umm, the density of air in an OPEN tube won't change if you constrict it; if you decrease the radius, the cylinder will encompass LESS air since air will just flow out. The only way the density of air changes is if you constrict a closed air-filled can or take an open can to Jupiter.
But yeah, if you do have denser air inside the tube, sound velocity will be lower and your fundamental frequency will be lower.
So for the same air medium, changing the width of the pipe won't affect fundamental frequency

 

[mehc012]

In the Berkley Review it says that "Width of the pipe has no impact on the frequency of resonance waves".

Just trying to understand why?

Frequency = nv/2L for an open tube or standing wave.

But if the width of the pipe is smaller, then wouldnt the density of the particles increase? (Smaller volume, same number of particles/mass).

and the speed of a sound wave is inversely proportional to the density of the gas particles. v = root (vP/density)


What am i missing here?

You are making an assumption of equal number of particles in the larger pipe. Is that supported by the question at hand (the full Q is not posted, so I am legitimately asking).