The node.
If the frequency stays the same, then the wavelength stays the same.
Nothing happens
Wavelength is halved.
the frequency of the wave increases.
the frequency of the wave increases.
it stays the same
Nothing happens
Wavelength decreases.
It stays the same.
It stays the same.
The wave length would necessarily be one half. The speed would remain the same independent of the frequency.
As long as the wave stays in the same medium, the product of its wavelength and frequency is always the same number ... its speed.