Spherical Wave - What is the phase?

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SUMMARY

The discussion focuses on calculating the phase of a spherical wave emitted from the origin with a wavelength of 2.0 m. At a distance of r=4.0 m, the phase is given as pi radians. The objective is to determine the phase at r=3.5 m using the wave equation D(x,y,z,t)=Asin(kr-wt+phi), where k=(2pi)/(lambda) and w=(2pi)/T. The initial attempts to solve the problem involved incorrect substitutions and manipulations of the wave equation.

PREREQUISITES
  • Understanding of wave equations, specifically D(x,y,z,t)=Asin(kr-wt+phi)
  • Knowledge of wave parameters: wavelength, phase, and displacement
  • Familiarity with the concepts of wave number (k) and angular frequency (w)
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the derivation and application of the wave equation D(x,y,z,t)=Asin(kr-wt+phi)
  • Learn how to calculate wave number (k) and angular frequency (w) for different wave types
  • Explore phase relationships in spherical waves and their implications
  • Practice solving similar problems involving phase calculations in wave mechanics
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Students studying physics, particularly those focusing on wave mechanics, as well as educators looking for examples of phase calculations in spherical waves.

samee
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Homework Statement



A spherical wave with a wavelength of 2.0 m is emitted from the origin. At one instant of time, the phase at r=4.0m is pi radians. At that instant, what is the phase at r=3.5m?

Homework Equations



D(x,y,z,t)=Asin(kr-wt+phi)
k=(2pi)/(lambda)
w=(2pi)/T

The Attempt at a Solution



(kr-wt+(phi))=phase constant
D(x,y,z)=displacement, or here, radius
A cancels and doesn't matter.
4/(pi)=3.5/x
x=3.5(pi)/4 <---- which is wrong.

So then I tried subtracting the equations...
4=Asin(pi)
-3.5=-Asinx
.5=Asin(pi)-Asinx
.5=Asinx <---- Then I didn't know what to do with it. Help please?
 
Last edited:
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Nevermind . . .
 
I'd sure like to know.
 

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