# Why do two tubes with different lengths produce different frequencies?

I've learned that it has to do with harmonic frequencies and the relationship between length and wavelength in the equation $L = n(\frac{\lambda}2)$, but my question is why?

If you were to blow air into two tubes that differ only in length, the result would be two different frequencies. But this applies even if you are blowing air in exactly the same way for both tubes (equal velocity, quantity, pressure, etc.). This should mean that the motion of the particles in each tube should be the same, and although the wave speed is the same, frequencies and wavelengths are different. How does changing the location of the tube's bottom cause this when the particles at the top have no direct interactions with it?

This question also applies to the idea of changing the frequency of a vibrating string by changing the location of one end (holding it down with your finger).