Two waves executing simple harmonic motion travelling in the same...

When two waves of the same frequency superimpose, the resultant amplitude is given by

${A}_{resultant} = \sqrt{{A}_{1}^{2} + {A}_{2}^{2} + 2{A}_{1}{A}_{2}cosϕ}$

$⇒ \sqrt{3}A = \sqrt{{A}^{2} + {A}^{2} + 2{A}^{2}cosϕ}$

$⇒ 3{A}^{2} = 2{A}^{2} + 2{A}^{2}cosϕ$

$⇒ cosϕ = \dfrac{1}{2}$

$∴ ϕ = 60 °$

$∴$Phase difference $= 60$ degree