Transverse Wave Homework Problem

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SUMMARY

The discussion centers on calculating the transverse speed of a wave described by the function y(x, t) = (15.0 cm) cos(πx - 12πt). The maximum transverse velocity is determined using the formula v_max = ωA, where ω is the angular frequency and A is the amplitude. Given that the amplitude A is 15.0 cm and the angular frequency ω is 12π rad/s, the maximum transverse speed is calculated as 12π * 15.0 cm. The user seeks assistance in determining the transverse speed at a specific displacement of 12.0 cm.

PREREQUISITES
  • Understanding of wave equations and their components
  • Knowledge of angular frequency and amplitude in wave mechanics
  • Familiarity with calculus, particularly derivatives for velocity calculations
  • Basic trigonometry for interpreting cosine functions
NEXT STEPS
  • Calculate the transverse speed using the formula v = ωA for given values
  • Explore the concept of angular frequency in wave mechanics
  • Study the relationship between displacement and wave properties
  • Review examples of wave motion problems to enhance problem-solving skills
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Students studying physics, particularly those focusing on wave mechanics, as well as educators looking for examples of wave speed calculations in homework problems.

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Homework Statement


The function y(x, t) = (15.0 cm) cos([tex]\pi[/tex]x - 12[tex]\pi[/tex]t), with x in meters and t in seconds, describes a wave on a taut string. What is the transverse speed for a point on the string at an instant when that point has the displacement y = 12.0 cm?


Homework Equations


I know that the equation of the wave is given above and the max transverse velocity is w*A and the max transverse acceleration is w^2*A and I know how to get the velocity of the wave in the x direction (propagation)




The Attempt at a Solution


I'm not sure where to even start, I think I need to find where 12.0cm is in reference to either distance or time, then I could just plug it into the wave equation, I'm just not sure how to get there. Any help would be greatly appreciated!
 
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