A string is producing transverse vibration whose equation is y=0.… - Vidyadip

MCQ

A string is producing transverse vibration whose equation is $y=0.021 \sin (x+30 t)$, Where $x$ and $y$ are in meters and $t$ is in seconds. If the linear density of the string is $1.3 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$, then the tension in the string in $N$ will be

A
$10$
B
$0.5$
C
$1$
✓
$0.117$

✓

Answer

Correct option: D.

$0.117$

$y=0.021 \sin (x+30 t) \Rightarrow v=\frac{\omega}{k}=\frac{30}{1}=30 \mathrm{~m} / \mathrm{s}$.
Using, $v=\sqrt{\frac{T}{m}} \Rightarrow 30=\sqrt{\frac{T}{1.3 \times 10^{-4}}} \Rightarrow T=0.117 \mathrm{~N}$

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