# A certain organ pipe resonates in its fundamental mode at a frequency of 500 Hz in air. What will be the fundamental frequency if the air is replaced

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A certain organ pipe resonates in its fundamental mode at a frequency of 500 Hz in air. What will be the fundamental frequency if the air is replaced by hydrogen at the same temperature? The density of air is 1.20kgm^-3 and that of hydrogen is 0.089 kgm^-3.

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Suppose the speed of sound in hydrogen in v_h and that in aire is v_a. The fundamental frequency of an organ pipe is proportioN/Al to the speed of sound in the gas contained in it. If the fundamental frequency with hydrogen in the tube is v we have
v/(500Hz)=v_h/v_a=sqrt(rho_a/rho_h)=sqrt(1.2/0.089)=3.67
or v=3.67xx500Hz~~1840Hz`.