Solve Wave Superposition: 2Asin(7π(x+vt)) cos (3π(x+vt)) at t=0

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SUMMARY

The discussion focuses on solving the wave superposition equation 2Asin(7π(x + vt)) cos(3π(x + vt)) at time t=0 for maximum and minimum displacement locations. The participants confirm the equation's validity and explore critical points by differentiating the resultant wave function. The user initially struggles with graphing due to calculator limitations but resolves the issue by fixing the calculator, allowing for further analysis of critical points.

PREREQUISITES
  • Understanding of wave mechanics and superposition principles
  • Familiarity with trigonometric identities and calculus for differentiation
  • Knowledge of critical points and their significance in wave functions
  • Ability to use graphing calculators or software for visualizing functions
NEXT STEPS
  • Study wave superposition principles in greater detail
  • Learn how to differentiate trigonometric functions effectively
  • Explore graphing techniques for complex wave functions
  • Investigate the impact of amplitude and wavelength on wave behavior
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators and anyone interested in understanding wave superposition and critical point analysis.

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Homework Statement


Two waves are produced on a string with length of 1m. Wavelength of one is .5m Wavelength of the other is .2m. Amplitude and velocity are the same.
Show that 2Asin(7pi(x + vt)) cos(3pi(x + vt)).
At t=0 what locations are the max/min displacement at?

Homework Equations





The Attempt at a Solution


I can solve the first part no problem. We have Eq we needed to show. Then I take z'(x) and have 2pi*A(2cos(4pi*x)+5cos(10pi*x)) and = 0 to get crit points.. This is where I am stuck. My calculator is unable to compute the graph at such small y apparently. I was unfortunately unable to find anything on the internet on how to solve this. Any help would be greatly appreciated.
 
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So you I fixed my calculator, problem solved ><
 

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