A spherical wave with a wavelength of 2.0 m is emitted from the origin. At one instant of time, the phase at r = 4.0 m is p rad. At that instant, what is the phase at r = 3.5 m and at r = 4.5 m?

Short Answer

Expert verified

The phase at r=3.5mis 12πrad.

The phase atr=4.5mis32πrad.

Step by step solution

01

Given information

The wavelength of the wave is λ=2.0m

The phase atr=4.0misϕ1=πrad

02

The phase at r=3.5 m.

The phase difference is given by ϕ2-ϕ1=2πλr2-r1.

Substitute the given values

ϕ2-π=2π23.5-4.0ϕ2=-0.5π+πϕ2=12πrad

Therefore, phase difference atr=3.5mis12πrad.

03

The phase at r=4.5 m

Substitute the given values into ϕ2-ϕ1=2πλr2-r1.

ϕ2-π=2π24.5-4.0ϕ2=0.5π+πϕ2=32πrad

Therefore, the phase atr=4.5mis32πrad.

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