The fundamental frequency of vibration of a string stretched between two rigid support is $50\,Hz$. The mass of the string is $18\,g$ and its linear mass density is $20\,g / m$. The speed of the transverse waves so produced in the string is $..........\,ms ^{-1}$
JEE MAIN 2023, Medium
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Fundamental frequency $=50\,Hz$
$\frac{mass}{length}$=$\frac{20 g}{m}$
mass$=18\,g$
length of string $=\frac{18}{20} m =\frac{9}{10} m$
from diagram $\frac{\lambda}{2}=\ell$
$\Rightarrow \lambda=2 \ell=\frac{9}{5}\,m$
again speed $v=f \lambda=50 \times \frac{9}{5}=90\,m / s$
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