I don't know exactly what does 2nd order antinode mean. If it would be the 1st antinode in the 2nd harmonic of the standing wave, the following should be true:
And it doesn't make sense.
If the 2nd order antinode means the 2nd antinode for a certain harmonic [n], then the following holds:
Or
And neither of both makes sense, since [n] should be an integer.
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