Discussion
A steel wire 1.2 m long has a mass of \(4.8 \times 10^{-3}\) kg. If the wire is under a tension of 10 N, then the speed of transverse waves on the wire is:
Answer: C
The speed of a transverse wave on a stretched string is \(v = \sqrt{T/\mu}\), where \(\mu\) is the mass per unit length.
\[ \begin{aligned} \mu = \frac{4.8 \times 10^{-3}}{1.2} \\ &= 4 \times 10^{-3}\ \text{kg/m} \end{aligned} \]
\[ \begin{aligned} v = \sqrt{\frac{10}{4 \times 10^{-3}}} \\ &= \sqrt{2500} = 50\ \text{m/s} \end{aligned} \]
The other speeds would need a tension of 3.6 N, 6.4 N or 14.4 N respectively for this wire, so only 50 m/s fits 10 N. The answer is option C.
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