The fundamental frequency of vibration of a string stretched betw… - Vidyadip

MCQ

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 $..........\,ms ^{-1}$

✓
$90$
B
$45$
C
$30$
D
$15$

✓

Answer

Correct option: A.

$90$

a
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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