Question

Two guitar strings, of equal length and linear density, are tuned such that the second harmonic of the first string has the same frequency as the third harmonic of the second string. The tension of the first string is 510 N. Calculate the tension of the second string.

Answer 1

Answer:

The tension in the second string is 226.7 N.

Explanation:

Length is L, mass per unit length = m

T = 510 N

Let the tension in the second string is T'.

second harmonic of the first string = third harmonic of the second string

$2 f = 3 f'\\\\2\sqrt{\frac{T}{m}} = 3 \sqrt {\frac{T'}{m}}\\\\4 T = 9 T'\\\\4\times 510 = 9 T'\\\\T' = 226.7 N$