Why Do Standing Waves Require Specific Wavelength Conditions?

[suspenc3]

Why do standing waves only exist when $$\lambda=2L/n$$? For example why don't they exist when $$\lambda=4L$$

Not really sure but if $$\lambda$$ equals 4L then there is only going to be one "loop", I am guessing this has somehting to do with it but I am not sure how to explain it.

 

[chroot]

Generally, a standing wave exists when the reflection of the wave from one end of the cavity reinforces the wave already present in the cavity. The generally means the ends of the cavity need to be nodes to support a standing wave. When the wavelength is one-quarter of the length of the cavity, it will not be self-reinforcing, and will decay. This is because nothing "special" happens at one-quarter of the wavelength; compare to the point at half the wavelength, where there is a node.

- Warren