The transverse displacement in a streched string is given by y = … - Vidyadip

MCQ

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 ..... $N$

✓
$648$
B
$650$
C
$649$
D
$651$

✓

Answer

Correct option: A.

$648$

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

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

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

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