Discussion
The speed of the transverse waves on a steel wire of length 50 cm and mass 5 g subjected to a tension of 64 N is
Answer: C
The wave speed is 80 m s-1.
The speed of a transverse wave on a string is \(v = \sqrt{T/\mu}\), where \(\mu\) is the mass per unit length.
\[ \begin{aligned} \mu &= \frac{0.005\ \text{kg}}{0.5\ \text{m}} = 0.01\ \text{kg/m} \\ v &= \sqrt{\frac{64}{0.01}} = \sqrt{6400} = 80 \end{aligned} \]
Dividing 5 g by 50 cm without converting units gives \(\mu = 0.1\) and \(v = \sqrt{640} = 8\sqrt{10}\), option B. Only the SI values, 0.005 kg over 0.5 m, give the right \(\mu\).
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