A certaain string on a piano is turned to produce middle C(f=261.63 Hz) by adjusting tension in the string.?

For fixed wavelength, what is the frequency when this tension is doubled?

A certaain string on a piano is turned to produce middle C(f=261.63 Hz) by adjusting tension in the string.?
Frequency is proportional to the square root of tension.


http://en.wikipedia.org/wiki/Pitch_(musi...





f \propto \sqrt{T} and for this case 261.63 \propto \sqrt{T}





So, if the tension is doubled.


f ' \propto \sqrt{2T}





By ratios, 261.63 / f ' = sqrt {T} / sqrt {2T}





f ' = (sqrt {T} / sqrt {2T}) / 261.63