Question

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

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

Answer 1

Answer: (B)

40 cm

Answer 2

Fundamental frequency $\upsilon = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$
$\upsilon \propto \frac{1}{L} \, \therefore \frac{800}{1000} = \frac{L'}{50}$
$L' = \frac{800 \times 50}{1000} = 40 \, cm$