How to Prove AI = AT + AR for Wave Amplitudes?

  • Context: Undergrad 
  • Thread starter Thread starter Aaron8153
  • Start date Start date
  • Tags Tags
    Amplitudes String
Click For Summary
SUMMARY

The discussion centers on proving the equation AI = AT + AR, where AI, AT, and AR represent the amplitudes of incident, transmitted, and reflected waves, respectively. The conservation of energy principle, represented by W1 = W2, is crucial for this proof. The wave equations provided, yI(x,t), yR(x,t), and yT(x,t), illustrate the relationships between wave amplitudes and their respective velocities. Understanding how to calculate energy in a wave is essential for validating this equation.

PREREQUISITES
  • Understanding of wave mechanics, specifically wave equations.
  • Familiarity with the principle of conservation of energy in physics.
  • Knowledge of amplitude and its significance in wave behavior.
  • Basic grasp of wave velocity and its relationship to frequency and wavelength.
NEXT STEPS
  • Research the mathematical derivation of wave energy calculations.
  • Study the relationship between wave amplitude and energy in different mediums.
  • Explore the implications of conservation laws in wave physics.
  • Learn about the effects of wave interference on amplitude and energy distribution.
USEFUL FOR

Students and professionals in physics, particularly those focusing on wave mechanics, energy conservation, and related mathematical proofs in wave theory.

Aaron8153
I know that:
yI(x,t) = AI sin [k1( x - v1t )]
yR(x,t) = AR sin [k1( x - v1t )]
yT(x,t) = AT sin [k1( x - v2t )]

W1 = W2
k1v1 = k2v2

I am unsure about how to prove that AI = AT + AR
Where AI, AT, and AR are the different amplitudes of the incident, transmitted, and reflected waves.
 
Science news on Phys.org
Basically, it's that "W1 = W2" which, I take it, is "conservation of energy". Do you know how to calculate the energy in a wave?
 

Similar threads

Reflection and Transmission of String Waves
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Standing Waves by Reflection: Losses of the Reflected Wave
  • · Replies 16 ·
Replies
16
Views
3K
Progressive harmonic wave & reflection / transmission
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad How Do I Prove Polynomials Span P2?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Two standing waves forming a traveling wave
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Transverse Wave in a String Reflection and Transmission
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Confusion With Derivation of Fresnel Equations
  • · Replies 1 ·
Replies
1
Views
3K
Standing wave transverse motion and amplitude
  • · Replies 5 ·
Replies
5
Views
2K
Superposition of Two Waves on a String: Amplitude and Wavelength Calculation
  • · Replies 1 ·
Replies
1
Views
2K
Solve Superposition Wave: Prove, Phase Angle & Amplitude
  • · Replies 10 ·
Replies
10
Views
2K