Two strings X and Y of a sitar produce a beat frequency 4 Hz. 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

(1) 296 Hz

(2) 298 Hz

(3) 302 Hz

(4) 304 Hz

(1)

x = beat frequency = 4 Hz, which is decreasing (4 → 2)

after increasing the tension of the string y.

Also tension of wire y increasing so ${n}_{y}\text{​}↑$ $\left(\because \text{\hspace{0.17em}}n\propto \sqrt{T}\right)$

Hence ${n}_{x}-{n}_{y}\text{​}↓=x\text{​}↓$ → Correct

${n}_{y}\text{​}↑-{n}_{x}=x\text{​}↓$ → Wrong

${n}_{y}={n}_{x}-x=300-4=296Hz$

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