Question

A string of length $lcm$ is clampled at both ends. Initially the string is resonating in 3rd harmonic. After some time, string resonates in 5th harmonic. The gap between nodes in 3rd harmonic is $10cm$ greater than gap between nodes in 5th harmonic. Length of string is

• A. 50 $cm$
• B. 60 $cm$
• C. 65 $cm$
• D. 75 $cm$

Answer 1

The correct option is D 75 $cm$

Gap between nodes $=\frac{l}{3}$

Gap between nodes $=\frac{l}{5}$
$\frac{l}{3}-\frac{l}{5}=10$
$\frac{5l-3l}{15}=10$
$l=75cm$