Question

A guitar string is struck and found to have a frequency of 2048 Hz.If both the tension and the length are doubled, what is the new frequency of the string?

Answer 1

Fundamental frequency :

f = (1/2L) √(T/p)

Where:

L = lenght

T = tension

p = mass

Frequency is inversely proportional to Lenght

Frequency is proportional to the square root of the tension

If both are doubled:

f'= f * (1/2) √2

f' = f / √2 = 2048 / √2 = 1448 HZ