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PART - 2 CH - 14 Waves — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 14 Waves2 Marks
Question
The string of a tunning fork and a tuning fork are played simultaneously. At length of the wire is kept at 0.49 meter or 0.50 meter. 4 beats per second are heared. what is the frequency of tunning fork?
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Answer

The frequency of the tunning fork for length of wire $l$ will be $==\frac{1}{2 l} \sqrt{\frac{T}{m}}$
Let the frequency of tunning fork = n. vibrating with tunning frok 4 beat/second will generate. Therefore, frequency of tunning frok will be (n+4) or (n-4). 0.49 meter lengths wire frequency will greater the 0.50 meter length's wire. There- fore the frequency of 0.49 meter wire will be n + 4 and the frequency of 0.50 meter wire will be n-4.
$\begin{aligned}\therefore \quad n+4 & =\frac{1}{2 \times 0.49} \sqrt{\frac{T}{m}}\ldots\ldots (1) \\n-4 & =\frac{1}{2 \times 0.50} \sqrt{\frac{T}{m}}\ldots\ldots (2)\end{aligned}$
Divide equation (1) and (2)
$\begin{array}{rlrl}& & \frac{n+4}{n-4} & =\frac{0.50}{0.49}=\frac{50}{49} \\\Rightarrow & & 49 n+196 & =50 n-200 \\\Rightarrow & 196+200 & =50 n-49 n \\\Rightarrow & & 396 & =n\end{array}$
Then frequency of tuning fork = 396 vibration/second

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