MCQ
A transverse wave propagating on the string can be described by the equation $y=2 \sin (10 x+300 t)$. where $x$ and $y$ are in metres and $t$ in second. If the vibrating string has linear density of $0.6 \times 10^{-3} \,g / cm$, then the tension in the string is .............. $N$
  • A
    $5.4$
  • $0.054$
  • C
    $54$
  • D
    $0.0054$

Answer

Correct option: B.
$0.054$
b
(b)

$y=2 \sin (10 x+300 t)$

$y=A \sin (k x+\omega t)$

$k=10, \quad \omega=300$

$\mu=0.6 \times 10^{-3}\,g / cm$

$\mu=\frac{0.6 \times 10^{-3} \times 10^{-3}}{10^{-2}}\,kg / m$

$\mu=6 \times 10^{-5}\,kg / m$

$K=\frac{\omega}{V}$

$V=\frac{\omega}{K}=\frac{30 p}{T p}=30\,m / s$

$V=\sqrt{\frac{T}{M}}$

$T=V^2 \times M$

$T=(30)^2 \times 6 \times 10^{-5}$

$=900 \times 6 \times 10^5$

$=5400 \times 10^{-5}$

$=0.0541\,N$

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