Two wires are fixed on a sonometer. Their tensions are in the ratio $$8$$ :$$1$$, their lengths are in the ratio $$36$$:$$35$$, the diameters are in the ratio $$4$$:$$1$$ and densities are in the ratio $$1$$:$$2$$. If the value of higher frequency is $$36Hz$$, then lower frequency is p×qHz, here both p and q are integers. The value of $$p-q$$ is

Question

Two wires are fixed on a sonometer. Their tensions are in the ratio $$8$$ :$$1$$, their lengths are in the ratio $$36$$:$$35$$, the diameters are in the ratio $$4$$:$$1$$ and densities are in the ratio $$1$$:$$2$$. If the value of higher frequency is $$36Hz$$, then lower frequency is p×qHz, here both p and q are integers. The value of $$p-q$$ is

Infinity Learn · Accepted Answer

Given,          $$T1T2=81$$,$$L1L2=3635D1D2=41$$,ρ$$1$$ρ$$2=12Let$$ μ$$1$$ and μ$$2$$ be the linear mass densities, then∴ μ$$1=$$π×$$D124$$×ρ$$1$$ and μ$$2=$$π×$$D224$$×ρ$$2$$            $$($$μ$$=$$ρ$$S)$$∴ μ$$1$$μ$$2=D1D22$$×ρ$$1$$ρ$$2=412$$×$$12=81$$∴ $$f1f2=L2L1$$×$$T1T2$$×μ$$2$$μ$$1=353681$$×$$18=3536$$           $$f=12LT$$μWe have                 $$f2$$>$$f1f2=36$$∴$$f1=35=7$$×$$5p=7$$ ; $$q=5$$ ⇒$$p-q=2$$

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