Question

On a violin, a correctly tuned string has a frequency of 490 Hz. If the string produces a sound at 540 Hz. when under a tension of 25,5 N, What should the tension be to produce the correct frequency?

Answer 1

Fundamental frequency is given by

$f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

So

$f\alpha \sqrt{T}\therefore \frac{f_2}{f_1}=\sqrt{\frac{T_2}{T_1}}$

in our case for $f_1=490Hz,T_1=?$

and for $f^{}=540Hz,T_2=255$

$\therefore \frac{490}{540}=\sqrt{\frac{255}{T_1}}\therefore T_1=\left(\frac{540}{490}\right)$

$=309N$ (approx)