Question

A wire of length 108 cm produces a fundamental note of frequency 256 Hz, when stretched by a weight of 1 kg. By how much its length should be increased so that its pitch is raised by a major tone, if it is now stretched by a weight of 4 kg?

Answer 1

Case I. Frequency of the fundamental note, v = 256 Hz

length of the wire, L = 108 cm

stretching force, T = 1 kg f 

Case II. Frequency of the major tone emitted

stretching force, T = 4 kg f

Let the length be increased by x. 

Increased length of the wire, i.e.,

Thus, the length should be increased by 84 cm.