Tension and frequency relationship on a violin

[CAF123]

There is an equation relating the tension in a string fixed between two nodes and the velocity of the traveling waves which form the allowed standing waves. It is T = v^2 (μ) where μ is the mass per unit length.

Am I correct in saying that if the tension in the string increases then frequency also increases? I say ths because v= fλ and if f increases then so does v and subsequently, by the above formula, T.

Thanks.

 

[The_Duck]

You are correct. This is how you tune the strings: by adjusting their tension.