I don't quite understand why no interference would occur when the separation between the two sources is less than the wavelength of the wave. I can't find demonstrations about such special case on the internet.
The following is the homework which raised my question:
Suppose there are two speakers set up to demonstrate a two-source wave interference. The speakers are connected to the same signal generator to generate coherent sound waves at frequency $500Hz$ and wavelength $0.68m$. The distance between the two speakers is $0.45m$. The distance between the speakers and the observing line XY is $2m$.
Explain why neither a maximum or minimum is detected along XY.
The homework solution is:
Since the separation between the two speakers is $0.45m$ which is shorter than the wavelength, the path difference at any point on XY must be less than one wavelength. Thus no interference occurs.
But how and why??
Does this statement mean the observer would hear a constant amplitude (amplitude of a single speaker) of sound along the XY? This doesn't make sense to me.
Is there any graphical illustration I can refer to?
Also, shouldn't there always be an anti-nodal line with path difference of $0$ at the centre? Shouldn't there always be constructive interference along this line?
Please enlighten me! Thanks in advance!!