I have done a handful of problems related to sound waves in air columns and one thing I have noticed is that, unless told otherwise in the problem formulation, one always assumes that sound wave that is formed is always the fundamental harmonic and thus the length of the air column comprises a half wavelength. What is the rationale behind this? I thought the shapes were somewhat arbitrary, depening on the context: How is one so sure that it most certainly is the fundamental harmonic? Why couldn't the sound wave have e.g. a 2nd harmonic or a 3rd harmonic shape? Example: In this case, the sound wave is regarded as a fundamental harmonic (read: must be regarded as the fundamental or else the answer turns out to be wrong). What argues for doing that? Example: In this example, one cannot assume that the shape of the sound wave is the "fundamental" (i.e. anti-nodes at the ends and node in the middle of the tunnel). Instead, one has to be quite careful and consider the possible shapes. Can somebody please help me see things clearly?