Optics problem, adding quantities

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SUMMARY

The discussion focuses on solving the optics problem of summing two sinusoidal quantities: Y1 = sin(Wt) and Y2 = sin(Wt + 30 degrees). The user initially attempts to combine these using basic addition, resulting in an incorrect expression. The correct approach involves applying trigonometric identities to simplify the sum of sine functions, which is essential for accurately solving problems in optics related to wave interference.

PREREQUISITES
  • Understanding of trigonometric identities, specifically the sum-to-product identities.
  • Familiarity with sinusoidal functions and their properties.
  • Basic knowledge of wave mechanics in optics.
  • Ability to manipulate equations involving angular frequency (W) and phase shifts.
NEXT STEPS
  • Research trigonometric identities, particularly the sine addition formulas.
  • Study wave interference patterns in optics, focusing on constructive and destructive interference.
  • Explore the mathematical representation of waves, including the use of complex numbers in wave equations.
  • Learn about the application of sinusoidal functions in real-world optics problems.
USEFUL FOR

Students in physics, particularly those studying optics, as well as educators and anyone interested in understanding wave behavior and trigonometric applications in physical problems.

thezac11
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Homework Statement



-Find the sum of the two quantities:

Y1=sin(Wt) Y2=sin(Wt+30 degrees)

Homework Equations



Y(x,t)=AsinK(kx+Wt) <------- not sure if this is relevant

W=2(3.14)f , where f=frequency

The Attempt at a Solution



sin(Wt) + sin(Wt+30) = sin(Wt) + sin(Wt) + sin(30) = 2sin(Wt) + 0.5

-This is all I've got. I'm really not sure how to go about this problem, I know there something more to it than simply adding the quantities as I did. This problem is in the Optics section of my physics course, but I'm not sure how it relates to optics. Any help would be greatly appreciated.
 
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hi thezac11! :smile:
thezac11 said:
sin(Wt) + sin(Wt+30) = sin(Wt) + sin(Wt) + sin(30)

sorry, but that doesn't work at all :redface:

you need to look up your trigonometric identities :wink:​
 

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