The end correction of a resonance column is 1.0 cm. If the shortest length resonating with a tu

step 1 In this question we have given the end correction of a resonance column that is one semi and it

The end correction of a resonance column is 1.0 cm. If the...

The end correction of a resonance column is $1.0 \mathrm{~cm}$. If the shortest length resonating with a tuning fork is $14.0 \mathrm{~cm}$, the next resonating length is
(A) $44 \mathrm{~cm}$
(B) $45 \mathrm{~cm}$
(C) $46 \mathrm{~cm}$
(D) $47 \mathrm{~cm}$

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Key Concepts

Resonance in Air Columns

Resonance in air columns occurs when the dimensions of the column support standing sound waves that reinforce the sound energy. For tubes with one end closed and one end open, resonance happens when the air column’s effective length corresponds to an odd multiple of a quarter of the sound wavelength, resulting in strong, sustained vibrations at particular frequencies.

End Correction

End correction is an adjustment added to the measured physical length of an air column to account for the fact that the displacement antinode does not occur exactly at the open end of the tube. This correction is crucial in accurately determining the effective length over which the wave oscillates, and thus it affects the calculation of the wavelength and the resonant frequencies.

Harmonic Series in Closed Pipes

In closed pipes, where one end is closed and the other is open, only odd harmonics are present. This means resonance occurs at effective lengths of (2n + 1)?/4, where n = 0, 1, 2, etc. The fundamental resonance corresponds to n = 0 and higher resonances occur for successive odd multiples of the quarter wavelength, demonstrating the discrete set of allowed frequencies in such systems.

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