Both the strings, shown in figure are made of same material and h… - Vidyadip

MCQ

Both the strings, shown in figure are made of same material and have same cross$-$section. The pulleys are light. The wave speed of a transverse wave in the string $AB$ is $\nu_1$ and in $CD$ it is $\nu_2.$ Then $\frac{\nu_1}{\nu_2}$ is:

A
$1$
B
$2$
C
$\sqrt{2}$
✓
$\frac{1}{\sqrt{2}}.$

✓

Answer

Correct option: D.

$\frac{1}{\sqrt{2}}.$

$T_{AB} = T$
$T_{CD} = 2T$
where
$T_{AB}$ is the tension in the string $AB$
$T_{CD}$ is the tension in the stnng $CD$
The eelatlon between tension and the wave speed is given by
$\text{v}=\sqrt{\frac{\text{T}}{\mu}}$
$\text{v}\propto\sqrt{\text{T}}$
where
$v$ is the wave speed of the transverse wave
$\mu$ is the mass per unit length of the string
$\frac{\text{v}_1}{\text{v}_2}=\sqrt{\frac{\text{T}}{2\text{T}}}$
$=\frac{1}{\sqrt{2}}$

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