Recall the following trigonometric identity
Let and let . Here, corresponds to the harmonic, and . Then, the superposition of the two notes is So, the beat frequency is . The following table shows the value of for various values of . \begin{center}\begin{tabular}{|c|c|} \hline n & (in Hz)\\ \hline 1 & 183.292 \\ \hline 2 & 146.584 \\ \hline 3 & 109.876 \\ \hline 4 & 73.168 \\ \hline 5 & 36.46 \\ \hline 6 & 0.248 \\ \hline 7 & 36.956 \\ \hline \end{tabular}\end{center} So, clearly the smallest number of beats occurs when . Recall that a beat occurs whenever the second cosine factor equals or , therefore, the number of beats per second is . Therefore, answer (B) is correct. |

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