2
Question
A steel wire has a length of \(12~ m\) and a mass of \(2.10 ~kg\). What will be the speed of a transverse wave on this wire when a tension of \(2.06 \times 10^{4} N\) is applied?
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Solution
Given,
Length of the steel wire, \(L=12~ m\)
Mass of the steel wire, \(m=2.10 ~kg\)
Mass per unit length,
\(\mu=m/L=2.10/12=0.175~ kg/m\)
Velocity of the transverse wave, for tension \(T\)
\(v=\sqrt{\dfrac{T}{\mu}}\)
\( v=\sqrt{\dfrac{2.06\times10^{4}\times12}{2.10}}=\sqrt{\dfrac{1236\times10^{4}}{105}}\)
\(=\sqrt{11.77\times10^{2}}=3.43\times10^{2}\)
\(v=343.0 ~m/s\)
Final Answer: \(v=343.0 ~m/s\)
Length of the steel wire, \(L=12~ m\)
Mass of the steel wire, \(m=2.10 ~kg\)
Mass per unit length,
\(\mu=m/L=2.10/12=0.175~ kg/m\)
Velocity of the transverse wave, for tension \(T\)
\(v=\sqrt{\dfrac{T}{\mu}}\)
\( v=\sqrt{\dfrac{2.06\times10^{4}\times12}{2.10}}=\sqrt{\dfrac{1236\times10^{4}}{105}}\)
\(=\sqrt{11.77\times10^{2}}=3.43\times10^{2}\)
\(v=343.0 ~m/s\)
Final Answer: \(v=343.0 ~m/s\)
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