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 speed of transverse waves in a wire is calculated using the formula: $$v = \sqrt{\frac{T}{\mu}},$$ where: - $T$ is the tension in the wire, - $\mu$ is the mass per unit length. Step 1: Substitute the Given Values Given: $$T = 70 \, \text{N}, \quad \mu = 7.0 \times 10^{-3} \, \text{kg/m}.$$ Substitute into the formula: $$v = \sqrt{\frac{70}{7.0 \times 10^{-3}}}.$$ Step 2: Simplify the Calculation $$v = \sqrt{\frac{70}{0.007}} = \sqrt{10000}.$$ $$v = 100 \, \text{m/s}.$$ Final Answer: $$\boxed{100 \, \text{m/s}}$$