Question

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

• A. $100 \,ms^{-1}$
• B. $200 \,ms^{-1}$
• C. $400 \,ms^{-1}$
• D. $500 \,ms^{-1}$

Answer 1

Answer: (C)

Here, Length, $L = 10\, m$
Mass, $M = 5\, g = 5 \times 10^{-3}\, kg$
Tension, $T = 80\, N$
Mass per unit length of the wire is
$\mu = \frac{M}{L} = \frac{5 \times 10^{-3}\,kg}{10\,m}$
$= 5 \times 10^{-4}\,kg\,m^{-1}$
Speed of the transverse wave on the wire is
$v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{80\,N}{5 \times 10^{-4}\,kg\,m^{-1}}}$
$= 4 \times 10^{2}\,ms^{-1}$
$= 400\,ms^{-1}$