Physics -guitar string frequency and wavelength question?

v = √T/μ, where T:tension, μ:linear density

v = fλ, where f:frequency, λ:wavelength

Since the speed of sound wave is directly proportional

to string tension, increasing the tension results

in a higher speed wave. But by increasing string tension

we are restricting the large movement of the string from its

equilibrium postion and the wavelength of the standing

wave is smaller while its frequency increases.

Increasing tension increases the speed of sound in the string.

The wavelength of a standing wave is determined by the locations of the nodes, the places where the string is forced to be unmoving. Those don't change as you tighten the guitar string.

Speed = frequency * wavelength

Speed increases, wavelength is constant, so frequency...?