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  4. The length of a sonometer wire AB is 110 cm. Where should the two bridges be placed from A to divide the wire in three segments whose fundamental frequencies are in the ratio of 1:2:3

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Q. The length of a sonometer wire $AB$ is $110 \,cm.$ Where should the two bridges be placed from $A$ to divide the wire in three segments whose fundamental frequencies are in the ratio of $1:2:3$

JIPMERJIPMER 2016Waves

Solution:

Length of sonometer wire $(l)=110\, cm$
and ratio of frequencies $=1: 2: 3$.
Frequency $(v) \propto \frac{1}{l}$
or $l \propto \frac{1}{v}$.
Therefore $A C: C D: D B$
$=\frac{1}{1}: \frac{1}{2}: \frac{1}{3}=6: 3: 2$.
Therefore $A C=6 \times \frac{110}{11}=60\, cm$ and
$C D=3 \times \frac{110}{11}=30 \,cm$.
Thus $A D=60+30=90 \,cm$.