Solving Wave Equations with a Wall - Reflection and Amplitude

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SUMMARY

The discussion focuses on solving wave equations involving reflection at a boundary. The initial wave solution is given as u(x,t) = 3 cos(x - 345t), with a wavelength of 2π and an amplitude of 3m. When a wall is introduced at x=0, the task is to determine the form of the wave equation that includes both the incident and reflected waves, as well as to calculate the amplitude and phase of the reflected wave, ensuring that u(0,t) = 0. Key insights include the necessity of understanding wave reflection principles to derive the correct wave equation.

PREREQUISITES
  • Understanding of wave equations, specifically the form z(x,t) = Asin(ks-vt).
  • Knowledge of wave reflection principles and boundary conditions.
  • Familiarity with trigonometric functions and their properties.
  • Ability to analyze wave behavior in physical systems.
NEXT STEPS
  • Research the principles of wave reflection and transmission at boundaries.
  • Study the concept of phase shifts in wave mechanics.
  • Learn about superposition of waves and how to combine incident and reflected waves mathematically.
  • Explore graphical methods for visualizing wave interactions with boundaries.
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators and anyone interested in understanding wave behavior in the presence of boundaries.

inferno_gogo
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Homework Statement


We have waves propagating in the air. First part asks for a traveling wave solution in the x direction , given a wave length 2pi and amplitude 3m. I have obtained u(x,t) = 3 cos ( x - 345t). The question then asks what happens if a wall is placed at x=0, what is the form of u(x,t) including the reflect wave and incident wave. Also to find the amplitude and phase of the reflect wave given u(0,t) = 0.


Homework Equations


z(x,t)=Asin(ks-vt)


The Attempt at a Solution


I have hit a wall. No idea how to proceed with the form of the equation. Once I get that, I am pretty sure I will manage to find the phase shift and amplitude.
 
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inferno_gogo said:
I have hit a wall.

:biggrin: Then you should reflect! :biggrin:​

Hint: draw a diagram!

Draw the wave going through the wall as if it wasn't there.

Then turn one half of the wave round …

does it have the same frequency? the same amplitude? the same velocity? the same phase? :smile:
 

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