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Waves — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWaves5 Marks
Question
The length of a sonometer wire between two fixed ends is $110cm$. Where should the two bridges be placed so as to divide the wire into three segments, whose fundamental frequencies are in the ratio $1 : 2 : 3$?
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Answer

Here, total length of the wire
$1 = 110cm$
$V_1: V_2: V_3 = 1 : 2 : 3$
If $l_1, l_2, l_3$ are the length of these three parts as $\text{V}\propto\frac{1}{\text{l}}$
$\therefore \text{l}_2:\text{l}_2:\text{l}_3=\frac{1}{1}:\frac{1}{2}:\frac{1}{3}$
$=6:3:2$
Sum of the ratios = 11
$\therefore \text{l}_1=\frac{\text{L}}{1\text{l}}\times6=\frac{110}{11}\times6=60\text{cm}$
$\text{l}_2=30\text{cm}$
$\text{l}_3=20\text{cm}$
Hence, the bridges should be placed at 60cm and 90cm from the zero end of the wire.

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