Two sitar strings A and B playing the note 'D | vedclass

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(A) The frequency of a stretched string is given by $v = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$. Increasing the tension $T$ increases the frequency $v$. I

Vedclass · Accepted Answer

$422$

Vedclass · Answer

(A) The frequency of a stretched string is given by $v = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$. Increasing the tension $T$ increases the frequency $v$. Initially,the beat frequency is $|v_A - v_B| = 5 \; Hz$. Given $v_A = 427 \; Hz$,the possible values for $v_B$ are $427 - 5 = 422 \; Hz$ or $427 + 5 = 432 \; Hz$. When the tension of $B$ is increased,$v_B$ increases. If $v_B = 432 \; Hz$,increasing $v_B$ would make the difference $|427 - v_B|$ larger than $5 \; Hz$. If $v_B = 422 \; Hz$,increasing $v_B$ would make the difference $|427 - v_B|$ smaller,moving towards $427 \; Hz$. Since the beat frequency decreases to $3 \; Hz$,it confirms that $v_B$ was $422 \; Hz$ and it increased towards $427 \; Hz$.

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