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. The linear density of a vibrating string is $1.3 \times 10^{-4} \mathrm{~kg} / \mathrm{m} . \mathrm{A}$ transverse wave is propagating on the string and is described by the equation $\mathrm{Y}=0.021 \sin (\mathrm{x}+3 \circ \mathrm{t})$ where $\mathrm{x}$ and $\mathrm{y}$ are measured in meter and t in second. Ten sion in the string is A $\quad 0.12 \mathrm{~N}$ B $\quad 0.48 \mathrm{~N}$ C $1.20 \mathrm{~N}$ D $4.8 \mathrm{oN}$
. The linear density of a vibrating string is $1.3 \times 10^{-4} \mathrm{~kg} / \mathrm{m} . \mathrm{A}$ transverse wave is propagating on the string and is described by the equation $\mathrm{Y}=0.021 \sin (\mathrm{x}+3 \circ \mathrm{t})$ where $\mathrm{x}$ and $\mathrm{y}$ are measured in meter and t in second. Ten sion in the string is
A $\quad 0.12 \mathrm{~N}$
B $\quad 0.48 \mathrm{~N}$
C $1.20 \mathrm{~N}$
D $4.8 \mathrm{oN}$
Physics | Previous Year Question Papers
. The linear density of a vibrating string is $1.3 \times 10^{-4} \mathrm{~kg} / \mathrm{m} . \mathrm{A}$ transverse wave is propagating on the string and is described by the equation $\mathrm{Y}=0.021 \sin (\mathrm{x}+3 \circ \mathrm{t})$ where $\mathrm{x}$ and $\mathrm{y}$ are measured in meter and t in second. Ten sion in the string is
A $\quad 0.12 \mathrm{~N}$
B $\quad 0.48 \mathrm{~N}$
C $1.20 \mathrm{~N}$
D $4.8 \mathrm{oN}$

Correct option is
A $0.12 \mathrm{~N}$
Linear density $\mu=1.3 \times 10^{4} \mathrm{Kg} / \mathrm{m}$
Wave equation $y=0.021 \sin (x+30 t)$
Velocity of wave $\mathrm{v}=\frac{\omega}{\mathrm{k}}=\frac{30}{1}=30 \mathrm{~m} / \mathrm{s}$
$$
\begin{array}{l}
\text { Now } v=\sqrt{\frac{\mathrm{T}}{\mu}} \\
30=\sqrt{\frac{\mathrm{T}}{1.3 \times 10^{4}}} \\
\mathrm{~T}=11.7 \times 10^{-2} \\
\mathrm{~T}=0.117 \mathrm{~N} \approx 0.12 \mathrm{~N}
\end{array}
$$

i

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