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14.Waves and Sound
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A $10\, m$ long steel wire has mass $5\,g$. If the wire is under a tension of $80\, N$, the speed of transverse waves on the wire is .... $ms^{-1}$
A
$100$
B
$200$
C
$400$
D
$500$
Solution
Here, Length, $L=10 \mathrm{\,m}$
Mass, $\mathrm{m}=5 \mathrm{\,g}=5 \times 10^{-3} \mathrm{\,kg}$
tension, $\mathrm{T}=80 \mathrm{\,N}$
Mass per unit length of the wire is
$\mu=\frac{M}{L}=\frac{5 \times 10^{-3} \mathrm{\,kg}}{10}=5 \times 10^{-4} \mathrm{\,kgm}^{-1}$
Speed of the transverse wave on the wire is
$v=\sqrt{\frac{T}{\mu}}=\sqrt{\frac{80 N}{5 \times 10^{-4} \mathrm{\,kgm}^{-1}}}$
$=4 \times 10^{2} \mathrm{\,ms}^{-1}=400 \mathrm{\,ms}^{-1}$
Standard 11
Physics
