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Q.

A tuning fork produces a wave of wavelength 110 cm in air at 0⁰C. The wavelength at 25^oC would be

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a

110 cm

b

115 cm

c

120 cm

d

130 cm

answer is B.

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Detailed Solution

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$v = \sqrt{\frac{γRT}{M}} \Rightarrow v \propto \sqrt{T} \Rightarrow λ \propto \sqrt{T}$

$\frac{λ_{2}}{λ_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} \Rightarrow \sqrt{\frac{273 + 27}{273}} = {(1 + \frac{25}{273})}^{1 / 2}$

$\frac{λ}{110} = 1 + \frac{25}{546} \Rightarrow λ = 110 (1 + \frac{25}{546})$

$\approx 110 + 110 \frac{25}{550} \approx 115 cm$

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A tuning fork produces a wave of wavelength 110 cm in air at 00C. The wavelength at 25oC would be