A steel wire with mass per unit length $$7.0 \times 10^{-3} \text{ kg m}^{-1}$$ is under tension of 70 N. The speed of transverse waves in the wire will be:

We need to find the speed of transverse waves in a steel wire under tension.

The mass per unit length is $$\mu = 7.0 \times 10^{-3}$$ kg/m and the tension is $$T = 70$$ N. The speed of transverse waves in a string is given by $$v = \sqrt{\frac{T}{\mu}}$$, a formula derived from Newton’s second law applied to a small element of the string, where tension provides the restoring force and linear mass density represents inertia.

Substituting the given values yields $$v = \sqrt{\frac{70}{7.0 \times 10^{-3}}} = \sqrt{\frac{70}{0.007}} = \sqrt{10000} = 100 \text{ m/s}$$.

The correct answer is Option B: $$100$$ m/s.