To determine the speed of a transverse wave on a string, we can use the formula: \[ v = \sqrt{\frac{T}{\mu}} \] where: - \( v \) is the speed of the wave, - \( T \) is the tension in the string (in Newtons), - \( \mu \) is the mass per unit length of the string (in kg/m). ### Step-by-Step Explanation 1. **Identify the Given Values**: - Tension \( T = 12 \, \text{N} \) - Mass per unit length \( \mu = 3 \times 10^{-2} \, \text{kg/m} \) 2. **Substitute the Values into the Formula**: We need to calculate the speed \( v \) using the formula provided. First, we will substitute the values of \( T \) and \( \mu \): \[ v = \sqrt{\frac{12 \, \text{N}}{3 \times 10^{-2} \, \text{kg/m}}} \] 3. **Calculate the Denominator**: Calculate \( \frac{T}{\mu} \): \[ \frac{12 \, \text{N}}{3 \times 10^{-2} \, \text{kg/m}} = \frac{12}{0.03} = 400 \, \text{m}^2/\text{s}^2 \] 4. **Take the Square Root**: Now, we take the square root of 400: \[ v = \sqrt{400} = 20 \, \text{m/s} \] ### Conclusion The speed of the wave propagation on the string is \( 20 \, \text{m/s} \). Therefore, the correct option is **B**. ### Explanation of Other Options - **Option A: 5 m/s**: This value is too low. If we consider the tension and mass per unit length, the calculated speed is much higher than this. - **Option C: 30 m/s**: This value is also incorrect. It does not match the calculated speed based on the given tension and mass per unit length. - **Option D: 40 m/s**: This value is too high. The tension and mass per unit length do not support such a high wave speed. ### Common Pitfalls - **Misunderstanding Units**: Ensure that the mass per unit length is in kg/m and tension is in Newtons. - **Calculation Errors**: Double-check arithmetic when calculating \( \frac{T}{\mu} \) and taking the square root. - **Ignoring the Formula**: Always start with the correct formula for wave speed on a string. ### Revision Summary - The speed of a transverse wave on a string is calculated using \( v = \sqrt{\frac{T}{\mu}} \). - For \( T = 12 \, \text{N} \) and \( \mu = 3 \times 10^{-2} \, \text{kg/m} \), the speed is \( 20 \, \text{m/s} \). - The correct answer is option B. - Always ensure units are consistent and double-check calculations to avoid errors.