Waves Part 2

Concept:Beat frequency is the absolute difference between two frequencies.Loading a tuning fork increases its mass and decreases its frequency.Explanation:Initial beat frequency = $\frac{8 \text{ beats}}{2 \text{ s}} = 4 \text{ Hz}$.So $|f_A - f_B| = 4 \text{ Hz}$.Given $f_B = 380 \text{ Hz}$, so $f_A$ is either $\mathbf{384 \text{ Hz}}$ or $\mathbf{376 \text{ Hz}}$. After loading, new beat frequency = $\frac{4 \text{ beats}}{2 \text{ s}} = 2 \text{ Hz}$.Loading decreases $f_A$ to $f_A' < f_A$.For the beat frequency to drop from $4 \text{ Hz}$ to $2 \text{ Hz}$, $f_A$ must have been higher than $f_B$ initially.If $f_A = 384 \text{ Hz}$, then after decreasing, say to $382 \text{ Hz}$, the difference becomes $2 \text{ Hz}$.If $f_A = 376 \text{ Hz}$, decreasing it would increase the difference, contradicting the drop.Thus original $f_A$ is $384 \text{ Hz}$.Answer:$f_A = 384$ Hz (Option A).