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Question Bank [ 2022 ] — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsQuestion Bank [ 2022 ]4 Marks
Question
Waves produced by two vibrators in a medium have wavelength $2\ m$ and $2.1\ m$ respectively. When sounded together they produce $8$ beats/second. Calculate wave velocity and frequencies of the vibrators.
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Answer

Given:
$\lambda_1=2 m , \lambda_2=2.1, n _1- n _2=8$
To find:
i. Wave velocity (v)
ii. Frequencies $\left(n_1\right.$ and $\left.n_2\right)$
Formula: $v=n \lambda$
Calculation:
From formula,
$v = n _1 \lambda_1= n _2 \lambda_2$
But $n _1- n _2=8$ ....(Given)
$ \therefore \frac{ v }{\lambda_1}-\frac{ v }{\lambda_2}=8$
$\therefore v \left(\frac{1}{2}-\frac{1}{2.1}\right)=8$
$\therefore v =\frac{8 \times 2 \times 2.1}{0.1}$
$\therefore v =336 m / s$
$\therefore n _1=\frac{ v }{\lambda_1}=\frac{336}{2}=168 Hz $
$\therefore n _2=\frac{ v }{\lambda_2}=\frac{336}{2.1}=160 Hz$
i. The wave velocity is $336\ m/s.$
ii. The frequency are $168\ Hz$ and $160\ Hz$.

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