Question

The fundamental (LaTeX: n=1 n = 1 harmonic or mode) frequency created on a stretched string with fixed ends occurs when the string is driven at a frequency of 50 Hz. If the tension in this string is doubled without changing its mass density, what would be the new fundamental frequency?

Answer 1

Answer:$\sqrt{2}f$

Explanation:

Given

Fundamental Frequency(f) is 50 Hz

and frequency is given by

$f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}---1$

Where T= tension

$\mu$=mass per unit length

if tension is doubled

$f'=\frac{1}{2L}\sqrt{\frac{2T}{\mu }}---2$

Divide 1& 2

$\frac{f}{f'}=\sqrt{\frac{T}{2T}}$

$f'=\sqrt{2}f$