The displacement of a particle of the medium wave is propagated through the medium is given y =Acos(ax+bt) whereA,a,b a positive constant and the wave is reflected by an obstacle at X equal to zero and the intensity of the reflected wave is 0.64 of the incident wave in the resultant wave formed after reflection is the maximum and minimum values of the particle in the medium

(a) KEY CONCEPT : Use the equation of a plane progressive wave which is as follows.
y = A cos (a x + b t)
Since the wave is reflected by an obstacle, it will suffer a phase difference of π. The intensity of the reflected wave is 0.64 times of the incident wave.
Intensity of original wave I ∝ A2
Intensity of reflected wave I’ = 0.64 I
⇒ I’ ∝ A’2⇒ 0.64 I ∝ A’2
⇒ 0.64 A2∝ A’2⇒ A’ ∝ 0.8A
So the equation of resultant wave becomes
y2= 0.8A cos (ax – bt + π) = -0.8A cos (ax – bt)