Question:

A 70cm70 \,cm long sonometer wire is in unison with a tuning fork. If the length of the wire is decreased by 1.0cm1.0\, cm, it produces 44 beats per second with the same tuning fork. The frequency of the tuning fork is

Updated On: Jun 14, 2022
  • 186 Hz
  • 220 Hz
  • 276 Hz
  • 312 Hz
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The Correct Option is C

Solution and Explanation

Let the frequency of the fork be nn.
In the first case, the length of the wire is 70cm70\, cm.
Therefore, n=12×70Tmn=\frac{1}{2 \times 70} \sqrt{\frac{T}{m}} \ldots (i)
On decreasing the length of the wire, its frequency will increase.
Hence, in the second case when the length is 69cm69\, cm,
then n+4=12×69Tmn+4=\frac{1}{2 \times 69} \sqrt{\frac{T}{m}} \ldots (ii)
Dividing Eqs. (i) by (ii), we get
nn+4=1/701/69\frac{n}{n+4}=\frac{1 / 70}{1 / 69}
nn+4=6970\Rightarrow \frac{n}{n+4}=\frac{69}{70}
70n69n=69×470 n-69 n=69 \times 4
n=276Hzn=276 \,Hz
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