Question

A string on musical instrument is $50cm$ long and its fundamental frequency is $270Hz$. If the desired frequency of $1000Hz$ is to be produced, the required string length in $cm$ is

• A. $13.5$
• B. $2.7$
• C. $5.4$
• D. $10.8$

Answer 1

The correct option is A $13.5$

Fundamental frequency = $\frac{v}{2L}$
$270=\frac{v}{2\times \left(50\right)}$
$v=270\times 100cm/s$
Now to make frequency $1000Hz$
$1000=\frac{v}{2\left(L\right)}$
$L=\frac{270\times 100}{2\times 1000}$
$\Rightarrow L=13.5cm$