Transverse displacement in a streched string is given by y = 0.06 sin , left( {frac{{2π }

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14.Waves and Sound

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The transverse displacement in a streched string is given by
$y = 0.06 \sin \, \left( {\frac{{2\pi }}{3}x} \right)\cos \,(120\pi t)$

where $x$ and $y$ are in $m$ and $t$ is in $s$. The length of the string is $1.5\, m$ and its mass is $3.0 \times 10^{-2} \,kg$, then tension in string is ..... $N$

A

$648$

B

$650$

C

$649$

D

$651$

Solution

$\omega=120 \pi, \mathrm{k}=\frac{2 \pi}{3}, \mathrm{v}=\frac{\omega}{\mathrm{x}}$

$\therefore \mathrm{v}=\frac{120 \pi}{2 \pi / 3}=180 \mathrm{\,m} / \mathrm{s}$

$\mathrm{T}=\mathrm{v}^{2} \mu=180 \times 180 \times \frac{3 \times 10^{-2}}{1.5}=648 \mathrm{\,N}$

Standard 11

Physics

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