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I have a question about the phenomena of diffraction.

Diffraction is said to be the bending of waves as they pass through a gap or around an object in the path of the wave. Diffraction occurs if the wavelength is greater than the distance across the gap through which it is traveling, or the width of the barrier it is traveling around.

I was wondering why the wavelength played a critical role in this. The wavelength is measured from peak to peak of two consecutive waves. If you therefore sent a single wave impulse through a gap would it have a defined wavelength and would it therefore diffract? This question has puzzled me for the last two weeks and no one seems to be able to come up with a sensitive answer so far. I therefore decided to try asking this question on some science forums.

Thank you

Sebastian