A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz . The length of the string producing a fundamental of 180 Hz will be _____ cm

Step-by-step solution

The formula to calculate the fundamental frequency produced in a vibrating string is given by f 0 = v 2 L       . . . 1 For the first case, it can be written that 120 = v 2 ( 90 )         . . . 2 Similarly, for the second case, it can be written that 180 = v 2 ( L )         . . . 3 Divide equation (3) by equation (2) and solve to obtain the required length of the string. 180 120 = v 2 L v 2 90 =   90 L ⇒ L =   90 × 120 180 = 60