The length of the wire between two ends of a sonometer is $$100$$ cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio $$1$$: $$3$$: $$5$$.

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Infinity Learn · Accepted Answer

Let $$L(=100$$ $$cm)$$ be the length of the wire and $$L1$$,$$L2$$ and $$L3$$ are the lengths of the segments as shown in the figure.  Fundamental frequency, v∝$$1L$$  As the fundamental frequencies are in the ratio of $$1$$:$$3$$ : $$5$$, ∴  $$L1$$:$$L2$$:$$L3=11$$:$$13$$:$$15=15$$:$$5$$:$$3$$  Let x be the common factor. Then $$15$$ $$x+5$$ $$x+3$$ $$x=L=100$$ $$23x=100$$   or   $$x=10023$$ ∴  $$L1=15$$×$$10023=150023$$ cm         $$L2=5$$×$$10023=50023$$ cm         $$L3=3$$×$$10023=30023$$ cm ∴ The bridges should be placed from A at $$150023$$ cm and $$200023$$ cm respectively.

The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1: 3: 5.

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