## University Physics with Modern Physics (14th Edition)

The fundamental frequency is given by equation 15.35. $$f_1=\frac{1}{2L}\sqrt{\frac{F}{\mu}}$$ In order to raise the pitch one octave, the fundamental frequency is multiplied by 2, so the tension F must be quadrupled, i.e., multiplied by 4. In order to raise the pitch two octaves, the fundamental frequency is multiplied by 4, so the tension F must be multiplied by 16. The danger in doing this is that the string/wire may snap under such a high tension.