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Q.

An organ pipe filled with oxygen gas at $47^{0} C$ resonates in its fundamental mode at frequency 300Hz. If it is now filled with nitrogen gas, at what temperature will it resonate at the same frequency in the fundamental mode?

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a

$87^{0} C$

b

$27^{0} C$

c

$107^{0} C$

d

$7^{0} C$

answer is A.

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Detailed Solution

$f = \frac{v}{2 l} and v \propto \sqrt{\frac{T}{M}} ∴ \frac{t + 273}{28} = \frac{47 + 273}{32} \Rightarrow t = 7^{0} C$

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An organ pipe filled with oxygen gas at 470C resonates in its fundamental mode at frequency 300Hz. If it is now filled with nitrogen gas, at what temperature will it resonate at the same frequency in the fundamental mode?