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A metallic wire of \( 1 \mathrm{~m} \) length has a mass of \( 10 \times 10^{-3} \mathrm{~kg} \). If a tension of \( 100 \mathrm{~N} \) is applied to a
wire, what is the speed of transverse wave ?
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wire, what is the speed of transverse wave ?
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Verified Answer
The correct answer is:
\( 100 \mathrm{~ms}^{-1} \)
Given, length of wire, \( I=1 \mathrm{~m} ; \) mass of wire, \( m=10 \times 10^{-3} \mathrm{~kg} \) tension, \( T=100 \mathrm{~N} \)
Speed of transverse wave, \( v=\sqrt{\frac{\text { Tension }}{\text { linear density }}} \)
Linear density
\[
\begin{array}{l}
=\frac{\text { mass }}{\text { length }}=\frac{10 \times 10^{-3}}{1}=10 \times 10^{-3} \\
\Rightarrow v=\sqrt{\frac{100}{10 \times 10^{-3}}}=\sqrt{10^{4}}=100 \mathrm{~ms}^{-1}
\end{array}
\]
Therefore, speed of transverse wave \( =100 \mathrm{~ms}^{-1} \)
Speed of transverse wave, \( v=\sqrt{\frac{\text { Tension }}{\text { linear density }}} \)
Linear density
\[
\begin{array}{l}
=\frac{\text { mass }}{\text { length }}=\frac{10 \times 10^{-3}}{1}=10 \times 10^{-3} \\
\Rightarrow v=\sqrt{\frac{100}{10 \times 10^{-3}}}=\sqrt{10^{4}}=100 \mathrm{~ms}^{-1}
\end{array}
\]
Therefore, speed of transverse wave \( =100 \mathrm{~ms}^{-1} \)
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