a travelling wave gets reflected at a boundary such that the ampitude of a reflected is half that of the incidemt wave. find the percentage of energy transmitted
Question
a travelling wave gets reflected at a boundary such that the ampitude of a reflected is half that of the incidemt wave. find the percentage of energy transmitted
Solution
The energy of a wave is directly proportional to the square of its amplitude.
Let's denote:
- Ai as the amplitude of the incident wave
- Ar as the amplitude of the reflected wave
Given that Ar = Ai/2, we can substitute this into the energy equation.
The energy of the incident wave (Ei) is proportional to Ai^2, and the energy of the reflected wave (Er) is proportional to Ar^2.
So, Ei = k * (Ai)^2 and Er = k * (Ar)^2, where k is the proportionality constant.
Substituting Ar = Ai/2 into the equation for Er gives Er = k * (Ai/2)^2 = k * Ai^2 / 4 = Ei / 4.
This means that the energy of the reflected wave is one fourth of the energy of the incident wave, or in other words, 25% of the incident wave's energy is reflected.
The transmitted energy (Et) is then the incident energy (Ei) minus the reflected energy (Er).
So, Et = Ei - Er = Ei - Ei/4 = 3Ei/4.
This means that 75% of the energy is transmitted.
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