Two identical piano wires kept under the same tension T

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Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be

For fundamental mode,

f =	1	√	T
	2l		m

Taking logarithm on both sides, we get

log f = log		1		+ log		√	T
		2l					μ

= log		1		+	1	log		T
		2l			2			μ

or log f = log			l		+	1	[logT - logμ]
			2l			2

Differentiating both sides, we get

	df	=	1		dT	(as and µ are constants)
	f		2		T

⇒	dT	= 2 ×	df
	T		T

Here df = 6
f = 600 Hz

∴	dT	=	2 × 6	= 0.02
	T		600