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Q.

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

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answer is 2.

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Detailed Solution

Given,          T1T2=81,L1L2=3635D1D2=41,ρ1ρ2=12Let μ1 and μ2 be the linear mass densities, then∴ μ1=π×D124×ρ1 and μ2=π×D224×ρ2            (μ=ρS)∴ μ1μ2=D1D22×ρ1ρ2=412×12=81∴ f1f2=L2L1×T1T2×μ2μ1=353681×18=3536           f=12LTμWe have                 f2>f1f2=36∴f1=35=7×5p=7 ; q=5 ⇒p-q=2
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