Q. A string on a musical instrument is $50\ cm$ long and its fundamental frequency is $270\ Hz.$ If the desired frequency of $1000\ Hz$ is to be produced, the required length of the string is
A) $13.5\ cm$
B) $2.7\ cm$
C) $5.4\ cm$
D) $10.3\ cm$
Explanation
(a) $n \propto \frac{1}{l} \Rightarrow \frac{l_{2}}{l_{1}} = \frac{n_{1}}{n_{2}} \Rightarrow l_{2} = l_{1}\left( \frac{n_{1}}{n_{2}} \right) = 50 \times \frac{270}{1000} = 13.5cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.