WAEC Physics 2013 Paper

Concept:The frequency of a vibrating string depends on the tension, length, and mass per unit length. For the same string, length and mass per unit length stay constant, so the frequency is proportional to the square root of the tension.Explanation:Let the original frequency be $f_1 = 14\text{ Hz}$ and the original tension be $T$.When the tension is quadrupled, the new tension is $T_2 = 4T$.Since frequency $f \propto \sqrt{T}$, we can write:$\frac{f_2}{f_1} = \sqrt{\frac{T_2}{T_1}}$Substitute $T_1 = T$ and $T_2 = 4T$:$\frac{f_2}{14} = \sqrt{\frac{4T}{T}} = \sqrt{4} = 2$Therefore, $f_2 = 2 \times 14 = 28\text{ Hz}$.The new frequency is twice the original frequency.Answer:The frequency when the tension is quadrupled is $28\text{ Hz}$. The correct option is C.