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Superposition of Waves — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsSuperposition of Waves3 Marks
Question
A stretched sonometer wire is in unison with a tuning fork. When its length is increased by 4 $\%$, the number of beats heard per second is $6.$ Find the frequency of the fork.
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Answer

Data : $\frac{L_2}{L_1}=1.04, n _1- n _2=6 Hz$
$ n _1=\frac{1}{2 L_1} \sqrt{\frac{T}{m}} \text { and } n _2=\frac{1}{2 L_2} \sqrt{\frac{T}{m}}$
$\therefore \frac{n_1}{n_2}=\frac{L_2}{L_1}=1.04$
$\therefore n _1=1.04 n _2 $
Now, $n_1-n_2=6$
$ \therefore 1.04 n _2- n _2=6$
$\therefore n _2=\frac{6}{0.04}=150 Hz$
$\therefore n _1= n _2+6=150+6=156 Hz $
This gives the frequency of the tuning fork as initially the wire and the fork vibrate in unison.

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