Q. The lowest resonant length for the resonance tube is . Find the next resonant length for the resonance tube. Consider the end correction of the resonance tube as .

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Solution:

In the concept of end correction, we also include the slight air column over the tube that is not a physical part of the tube because the source vibrates in the air and not inside the mouth of the tube.
End correction in a tube is given as where is the radius of the mouth of tube.
As per data given in question, here

Writing the equations for and harmonic repectively, we get

and

Solving these equations , we get