Question

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

• A. \( 100 \, \text{m/s} \)
• B. \( 50 \, \text{m/s} \)
• C. \( 10 \, \text{m/s} \)
• D. \( 200 \pi \, \text{m/s} \)

Hint:

The speed of transverse waves in a wire increases with the square root of the tension and decreases with the square root of the mass per unit length. Ensure accurate substitution and unit consistency for reliable results.

Answer 1

The Correct Option is A

The formula for the speed of transverse waves in a wire is \(v = \sqrt{\frac{T}{\mu}}\). Here, \( T \) represents the tension in the wire, and \( \mu \) denotes the mass per unit length. Step 1: Substitute the Given Values The provided values are \( T = 70 \, \text{N} \) and \( \mu = 7.0 \times 10^{-3} \, \text{kg/m} \). Substituting these into the formula yields: \[v = \sqrt{\frac{70}{7.0 \times 10^{-3}}}.\] Step 2: Simplify the Calculation \[v = \sqrt{\frac{70}{0.007}} = \sqrt{10000}.\] \[v = 100 \, \text{m/s}.\] Final Answer: \[\boxed{100 \, \text{m/s}}\]