A progrssive wave travels in a medium M_(1) and enters into another medium M_(2) in which its speed decreased to 75%. What is the ratio of the amplitude of the (a). Reflected and the incident waves , and (b). Transmitted and the incident waves ?

A progrssive wave travels in a medium M_(1) and enters into another me

1.	A progrssive wave travels in a medium M_(1) and enters into another medium M_(2) in which its speed decreased to 75%. What is the ratio of the amplitude of the (a). Reflected and the incident waves , and (b). Transmitted and the incident waves ?
Answer» Solution :Let `A_(i) , A_(r) and A_(t) ` be the amplitudes of the incidents , REFLECTED , and transmitted waves . GIVEN TAT , velocity in the medium refracted is `75%` of that in the initial medium. `v_(2) = (3)/(4) v_(1)` From Eqs. `(viii) and ( ix)` (a) `(A_(r))/(A_(i)) = ( v_(2) - v_(1))/( v_(2) + v_(1)) = (v_(2)/(v_(1)) -1)/((v_(2))/(v_(1)) + 1) = ((3)/(4) - 1)/((3)/(4) + 1) = -(1)/(7)` i.e., the required ratio is `\|(A_(r))/(A_(i))\| = 1 : 7` (B) `(A_(t))/( A_(i)) = ( 2 v_(2))/( v_(2) + v_(1)) = ( 2 v_(2)//v_(1))/(( v_(2))/(v_(1)) + 1) = (2 (3//4))/((3)/(4) + 1) = (6)/(7)` i.e., the required ratio is `\|(A_(t))/( A_(i))\| = 6 : 7`