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14.Waves and Sound
medium
The transverse displacement of a string (clamped at its both ends) is given by
$y(x,t)\, = \,0.6\,\sin \,\left( {\frac{{2\pi }}{3}x} \right)\,\cos \,(120\,\pi t)$
where $x$ and $y$ are in $metre$ and $t$ in $second$ . The length of the string is $1.5\,m$ and its mass is $3.0\times 10^{-2}\,kg$ the tension in the string will be .... $N$
A
$648$
B
$1248$
C
$324$
D
$162$
Solution
$\mathrm{V}=\frac{\omega}{\mathrm{K}}=\frac{120 \pi}{2 \pi / 3}=180 \mathrm{\,m} / \mathrm{s}$
$\mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mu}}$
$ \Rightarrow {\rm{T}} = {\rm{u}}{{\rm{V}}^2} = \left( {\frac{{3 \times {{10}^{ – 2}}}}{{1.51}}} \right) \times {(180)^2}$
$\quad=2 \times 10^{-2} \times 32400$
$=648 \mathrm{\,N}$
Standard 11
Physics
