Two sitar strings A and B playing the note ‘Dha’ are slightly out… - Vidyadip

Question

Two sitar strings A and B playing the note ‘Dha’ are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease to 3 Hz. What is the original frequency of B if the frequency of A is 427 Hz ?

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Answer

Increase in the tension of a string increases its frequency. If the original frequency of $B \left(v_B\right)$ were greater than that of $A \left(v_A\right)$, further increase in $v_B$ should have resulted in an increase in the beat frequency. But the beat frequency is found to decrease. This shows that $v_B<v_A$. Since $v_A-v_B=5 Hz$, and $v_A=427 Hz$, we get $v_B=422 Hz$.

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