Question

A guitar string is 90 cm long and has a fundamental frequency of 124 Hz. Where should it be pressed to produce a fundamatal frequecy of 186 Hz?

Answer 1

The fundamental frequency of a string fixed at both ends is given by
`v =(1)/(2L) sqrt((F)/(mu))`
As F and mu are fixed, `(v_1)/(v_2) = (L_2)/(L_1)` or , `L_2 = (v_1)/(v_2) L_1 = (124 Hz)/(186 Hz) (90 cm) = 60 cm.` Thus, the string should be pressed at 60 cm from an end.