Two simple harmonic waves having equal amplitudes of $$8$$ cm and equal frequency of $$10$$ Hz are moving along the same direction. The resultant amplitude is also $$8$$ cm. The phase difference between the individual waves is ______ degree.

Two SHM waves with equal amplitudes $$A = 8$$ cm and equal frequency $$f = 10$$ Hz move in the same direction. The resultant amplitude is also 8 cm, and we need to find the phase difference between them.

For two waves of equal amplitude $$A$$ with phase difference $$\phi$$, the resultant amplitude is given by $$A_R = \sqrt{A^2 + A^2 + 2A^2\cos\phi} = A\sqrt{2(1 + \cos\phi)} = 2A\cos\frac{\phi}{2}.$$

Substituting $$A_R = 8\text{ cm}$$ and $$A = 8\text{ cm}$$ yields $$8 = \sqrt{64 + 64 + 128\cos\phi},$$ which simplifies to $$64 = 128 + 128\cos\phi,\quad 128\cos\phi = -64,\quad \cos\phi = -\frac{1}{2}.$$

Therefore, $$\phi = \cos^{-1}\!\Bigl(-\tfrac{1}{2}\Bigr) = 120°,$$ so the phase difference is 120 degrees.