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  • When a stretched wire and a tuning fork are sounded together, Y beat per second are produced when length of wire is 85 cm or 90 cm, frequency of the fork 180 Hz. Find the value of y.<div class=

When a stretched wire and a tuning fork are sounded together, Y beat per second are produced when length of wire is 85 cm or 90 cm, frequency of the fork 180 Hz. Find the value of y.

Option: 1

4.1


Option: 2

5.1


Option: 3

5.6


Option: 4

5.3


Answers (1)

l_1=85 \mathrm{~cm} \quad l_2=90 \mathrm{~cm}\\ \text{frequency} \, n_2<n_1\\ \text{Now}\, n_1-n=y \quad eq - (1)\\ n-n 2=y \quad e q-(2)\\ \text {adding, we get}\\ n_1-n_2=2 y\\ \text{Also} \, \frac{n_1}{n_2}=\frac{l_2}{l_1}=\frac{90}{85}\\\\ \begin{aligned} & \frac{n_1}{n_2}=\frac{90}{85} \\ & n_1=\frac{90}{85} n_2\\ \end{aligned}\\ \text{from eq (3)}\\ \frac{90}{85} \, n_2-n_2=2 y\\ \text {eq (2)}\, y = n-n_2\\

\begin{aligned} & \frac{90}{85} \, n_2-n_2=2\left(n-n_2\right) \\ & \frac{90}{85} \, n_2-n_2=2 n-2 n_2 \\ & \frac{90 n_2}{85}-n_2+2 n_2=2 n\, \, \left [ \because n=180 \mathrm{Hz} \right ]\\ & \frac{90 n_2}{85}+n_2=180 \times 2 \\ & n_2\left[\frac{90}{85}+\frac{1}{1}\right]=360 \\ & n_2\left[\frac{90+85}{85}\right]=360 \\ & n_2\left[\frac{175}{85}\right]=360\\ & n_2=\frac{360 \times 85}{175} \\ & n_2=174.9 \, \mathrm{H.z} \\\ & e q \text { (2) } 180-174.9=y \\ & y=5.1 \end{aligned}

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Ramraj Saini

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