Two strings $X$ and $Y$ of a sitar produce a beat frequency $4Hz.$ When the tension of the string $Y$ is slightly increased the beat frequency is found to be $2\ Hz.$ If the frequency of $X$ is $300\ Hz,$ then the original frequency of $Y$ was

Question

Dr. Abubacker · Accepted Answer

(a) $n_{x} = 300Hz,\ n_{y} = \ ?$
$x =$ beat frequency $= 4\ Hz,$ which is decreasing $(4 \rightarrow 2)$ after increasing the tension of the string $y.$
Also tension of wire $y$ increasing so $n_{y} \uparrow (\because n \propto \sqrt{T})$
Hence $n_{x} - n_{y} \uparrow = x \downarrow \ \ \  \rightarrow Correct$
$n_{y} \uparrow - n_{x} = x \downarrow \ \  \rightarrow Wrong$
$\Rightarrow n_{y} = n_{x} - x = 300 - 4 = 296Hz$

Q. Two strings $X$ and $Y$ of a sitar produce a beat frequency $4Hz.$ When the tension of the string $Y$ is slightly increased the beat frequency is found to be $2\ Hz.$ If the frequency of $X$ is $300\ Hz,$ then the original frequency of $Y$ was

Explanation

Reviewed by Dr. Abubacker

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