# Two sources of waves are in phase and produce identical waves. These sources are mounted at the corners of a square and broadcast waves uniformly in all directions. At the center of the square, will the waves always produce constructive interference no matter which two corners of the square are occupied by the sources ?

Two sources of waves are in phase and produce identical waves. These sources are mounted at the corners of a square and broadcast waves uniformly in all directions. At the center of the square, will the waves always produce constructive interference no matter which two corners of the square are occupied by the sources ?
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Let us denote the length of the side of the square as a. Now, if you place the source on the corner of the square, the distance d that it travels is given by the Pythagorean theorem (d does not depend on the chosen corner due to the symmetry of the square)
${d}^{2}={a}^{2}+{a}^{2}\to d=\sqrt{2}a$
As we said, d does not the depend on the chosen corner. Furthermore, since the wave sources are in phase and produce identical waves, they will produce constructive interference at the centre of the square.