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Homework Help: Resultant equation of two identical out of phase waves

  1. Nov 23, 2016 #1
    1. The problem statement, all variables and given/known data
    Two identical traveling waves, moving in the same direction, are out of phase by π/5.0 rad. What is the amplitude of the resultant wave in terms of the common amplitude ym of the two combining waves? (Give the answer as the ratio of the total amplitude to the common amplitude.)

    2. Relevant equations
    Let y=ym.sinx be the equation of a wave where x is a variable time dependent. and ym is the maximum amplitude.
    Let y=ym.sin(x+ π/5.0) be the equation of a second identical wave but out of phase by π/5.0
    In trigonometric equations: sin(a)+sin(b)=2sin(0.5(a+b)).cos(0.5(a-b))

    3. The attempt at a solution
    the resultant equation will be:
    Y=ymsinx + ym.sin(x+ π/5.0)
    Y=ym(sinx + sin(x+ π/5.0))
    .............but sinx + sin(x+ π/5.0)=2sin(0.5(x+x+π/5.0)).cos(0.5(x-x-π/5.0))
    then Ym=2ym.cos(π/10.0) therefore Ym/ym=2 cos(π/10.0)=1.902
    is that correct ? and is that the ratio they want?
  2. jcsd
  3. Nov 24, 2016 #2
    Yes, this is correct. You may want to use LaTeX in the future to make your work more legible, but good work.
  4. Nov 24, 2016 #3
    What do you mean LateX? Is there another way to solve it?
  5. Nov 24, 2016 #4
    ##\LaTeX## is a formatting system for writing equations and papers that look nice. For example, instead of writing:
    Ym=2ym.cos(π/10.0) therefore Ym/ym=2 cos(π/10.0)=1.902
    You can write $$Y_m = 2y_m \cos{\left(\frac{\pi}{10}\right)} \Rightarrow \frac{Y_m}{y_m} = 2 \cos{\left(\frac{\pi}{10}\right)} = 1.902$$This can also be written inline with other text: ##Y_m = 2y_m \cos{\left(\frac{\pi}{10}\right)} \Rightarrow \frac{Y_m}{y_m} = 2 \cos{\left(\frac{\pi}{10}\right)} = 1.902## which is often useful. In the bottom left corner of the reply box there is a link to the forum LaTeX guide, which tells you how to do this in the forum (wrap standalone equations in "$$" without quotes and wrap inline equations with "##" without quotes).
  6. Nov 25, 2016 #5
    Okay I'll try it next time. Thanks :)
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