Question

A string in a musical instrument is $50cm$ long and its fundamental frequency is $800Hz$. If a frequency of $1000Hz$ is to be produced, then required length of string is

• A. $37.5cm$
• B. $40cm$
• C. $50cm$
• D. $62.5cm$

Answer 1

Answer: (B)

$40cm$

We know that for frequency of sound in string the formula is, $v=\frac{1}{2l}\sqrt{\frac{T}{m}}$ or $v\alpha \frac{1}{l}$
$\frac{v_1}{v_2}=\frac{l_2}{l_1}\Rightarrow \frac{800}{1000}=\frac{l_2}{50}$
$l_2=50\times \frac{800}{1000}=40cm$