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प्रश्न
A sonometer wire under suitable tension having specific gravity p, vibrates with frequency n in air. If the load is completely immersed in water the frequency of vibration of wire will become
पर्याय
`[(rho - 1)/("n"rho)]^(1/2)`
`"n"[(rho - 1)/(rho)]^(1/2)`
`"n"[(rho)/(rho - 1)]^(1/2)`
`[("n"rho)/(rho - 1)]^(1/2)`
उत्तर
`"n"[(rho - 1)/(rho)]^(1/2)`
Explanation:
The fundamental frequency of sonometer wire,
n = `1/(2"L") sqrt("T"/mu)`
As, L and µ are constant, so n depends on T.
`"n" prop sqrt"T"`
∴ `"n"_2/"n"_1 = sqrt("T"_2/"T"_1) = sqrt((("Weight")_"s" - ("Weight")_"w")/("Weight")_"s")`
`= sqrt(("V"rho_"s""g" - "V"rho_"w""g")/("V"rho_"s""g"))`
`= sqrt((rho_"s"/rho_"w" - 1)/(rho_"s"/rho_"w"))`
`= sqrt((rho - 1)/rho)`
(∵ specific gravity of sonometer wire, `rho = rho_"s"/rho_"w"`)
`"n"_2 = "n"sqrt((rho - 1)/(rho))`
