A sonometer wire $49 \mathrm{~cm}$ long is in unison with a tuning fork of frequency ' $n$ '. If the length…

A sonometer wire $49 \mathrm{~cm}$ long is in unison with a tuning fork of frequency ' $n$ '. If the length of the wire is decreased by $1 \mathrm{~cm}$ and it is vibrated with the same tuning fork, 6 beats are heard per second. The value of ' $n$ ' is
  1. $256 Hz$
  2. $288 Hz$
  3. $320 Hz$
  4. $384 Hz$

Solution

$\begin{array}{ll} & \mathrm{n}_1 \mathrm{~L}_1=\mathrm{n}_2 \mathrm{~L}_2 \\ \therefore & \mathrm{n}_1 \times 49=\mathrm{n}_2 \times 48 \\ \therefore & \mathrm{n}_2=\frac{49}{48} \mathrm{n}_1 \end{array}$ Given that, beat frequency, $\left|\mathrm{n}_1-\mathrm{n}_2\right|=6$ $\begin{array}{ll} \therefore & \left|\mathrm{n}_1-\frac{49}{48} \mathrm{n}_1\right|=6 \\ \therefore & \frac{\mathrm{n}_1}{48}=6 \\ \therefore & \mathrm{n}_1=288 \mathrm{~Hz} \end{array}$

Asked in: MHT CET 2023 (14 May Shift 2)

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