The phase difference between the two particles will be π/3 radians.
Explanation:
Let the wave equation of both the particles is,
x = Asin(ωt) and
x = Asin(ωt + Ф)
where A = amplitude = 20 cm for both the particles
ω = angular velocity = same for both the particles(because period is same)
Ф = phase difference.
Distance between the two particles is given by,
d = Asin(ωt + Ф) - Asin(ωt)
=> d = A[2sin(Ф/2)cos((2ωt+Ф)/2)]
clearly we will get a maximum value when cos((2ωt+Ф)/2) = maximum = 1
hence,
d = 2A[sin(Ф/2)]
=> 20 = 2x20[sin(Ф/2)]
=> [sin(Ф/2)] = 1/2
=> Ф/2 = π/6
=> Ф = π/3
Hence the phase difference between the two particles will be π/3 radians.