The length of the wire between two ends of a sonometer is

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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 of 1 : 3 : 5?

From formula, ƒ =	1	√	T
	x		m

⇒	1	∝ l
	ƒ

∴ l₁ : l₂ : l₃ =	1	:	1	:	1
	ƒ₁		ƒ₂		ƒ₃

= f₂ f₃ : f₁ f₃ : f₁ f₂
[Given: f₁ : f₂ : f₃ = 1 : 3 : 5]
= 15 : 5 : 3
Therefore the positions of two bridges below the wire are

	15 × 100	cm and	15 × 100 + 15 × 100	cm
	15 + 5 + 3		15 + 5 + 3

i.e.,	1500	cm,	2000	cm
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