How Does Phase Difference Influence the Amplitude of Combined Wave Functions?

AI Thread Summary
Phase difference significantly affects the amplitude of combined wave functions, particularly when two waves share equal wavelength and amplitude. The waves can be represented mathematically as y1(x) and y2(x), incorporating a phase difference φ. To find the resultant wave, y(x), one must sum the two wave equations and derive an expression for the amplitude based on A and φ. The question seeks a calculation of this amplitude, which involves understanding how the phase difference influences the overall wave amplitude. Ultimately, the relationship between amplitude and phase difference is crucial for analyzing wave interactions.
ColdFusion85
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I am not looking for any answers, just some guidance.

Consider case (c), (case (c) involved two waves with equal wavelength and amplitude, but with some arbitrary phase difference), and write the two waves as

y1(x) = Acos((\frac{2*\pi*x}{\lambda}))
y2(x) = Acos((\frac{2*\pi*x}{\lambda}) + \phi)

where \lambda and A are the common wavelength and amplitude of the two waves and \phi is their phase difference. Calculate the sum wave y(x) = y1(x) + y2(x) and find an expression for the amplitude of the sum wave in terms of A and \phi.

Find an expression for Amplitude in terms of the amplitude?? What exactly is this question asking?
 
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The question is asking you to calculate the amplitude of the sum wave given by the expression y(x) = y1(x) + y2(x). To do this, you will need to use the two given equations for y1(x) and y2(x), as well as the parameters A, λ, and ϕ. After calculating the sum wave, you can then use the equation for the amplitude of a wave (A = √(P/ρ)) to find an expression for the amplitude in terms of A and ϕ.
 
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