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 the

• A. $100m{s}^{-1}$
• B. $200m{s}^{-1}$
• C. $400m{s}^{-1}$
• D. $500m{s}^{-1}$.

Answer 1

The correct option is C $400m{s}^{-1}$

Here, Length, L $=10$m
Mass, M $=5g\times {10}^{-3}$kg
Tension, T $=80$ N
Mass per unit length of the wire is
$\mu =\frac{M}{L}=\frac{5\times {10}^{-3}kg}{10m}=5\times {10}^{-4}kg{m}^{-1}$

Speed of the transverse wave on the wire is
$\nu =\sqrt{\frac{T}{\mu }}=\sqrt{\frac{80N}{5\times {10}^{-4}kg{m}^{-1}}}$

$=4\times {10}^{2}m{s}^{-1}=400m{s}^{-1}$