Question

The frequency of a vibrating guitar string and its length have an inverse relationship. If a guitar string, 0.65 m long, vibrates four times per second, then the frequency of a string of length 0.5 metres is times per second.

Answer 1

Let the frequency of vibrating guitar string be $f$ when the length of a string is $l\text{m}$

Given: $l=0.65\text{m},f=4$ times per second.

From the question, we know that $f$ $\propto$ $\frac{1}{l}$
$\Rightarrow f=\frac{k}{l}$
$\Rightarrow 4=\frac{k}{0.65}$
$\Rightarrow k=4\times 0.65=2.6$
$\Rightarrow f=\frac{2.6}{l}$

when $l=0.5$ m

$\Rightarrow f=\frac{2.6}{0.5}=5.2$ times per second