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Addition of two waves

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  1. Jan 18, 2017 #1
    • Member advised to use the homework template for posts in the homework sections of PF.
    Two sinusoidal waves, identical except for phase, travel in the same direction along a string, producing the net wave

    y(x,t)=(5.5 mm)sin(12.0x -2.0 s-1 * t+0.390 rad),


    A. with x in meters and t in seconds. What is the wavelength λ of the two waves?
    B. What is the phase difference between them?
    C. What is their amplitude ym?


    I know A is .524 m but I am not too sure why. Other than that, I don't really know what I am doing. My general issue here is that I do not fully understand the form of the equation. Any information on what the different terms in the equation do would be helpful.

    I got the answer for A from (2pi)/12 btw. The 12 was the coefficient of the first term, but again I don't really understand what is happening here.
     
  2. jcsd
  3. Jan 18, 2017 #2

    haruspex

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    The wavelength is the smallest nonzero change in x which completes a cycle, i.e. changes the argument to the sine function by 2π.
    Write a general equation for a travelling wave. Write a second one which only differs in phase. Write the sum of the two.
    What trig formulae do you know that can put the sum of two sine functions in a different form? (These should be listed in the Relevant Equations section of the template. Oh, you didn't keep the template. Tut tut.)
     
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