Share
A spherical wave with a wavelength of 2.0 mm is emitted from the origin. At one instant of time, the phase at rrr = 4.0 mm is πradπrad. At t
Question
A spherical wave with a wavelength of 2.0 mm is emitted from the origin. At one instant of time, the phase at rrr = 4.0 mm is πradπrad. At that instant, what is the phase at rrr_1 = 3.5 mm ? Express your answer to two significant figures and include the appropriate units.
in progress
0
Physics
3 years
2021-09-05T07:07:30+00:00
2021-09-05T07:07:30+00:00 1 Answers
227 views
0
Answers ( )
Complete Question
A spherical wave with a wavelength of 2.0 mm is emitted from the origin. At one instant of time, the phase at r_1 = 4.0 mm is π rad. At that instant, what is the phase at r_2 = 3.5 mm ? Express your answer to two significant figures and include the appropriate units.
Answer:
The phase at the second point is![Rendered by QuickLaTeX.com \phi _2 = 1.57 \ rad](https://documen.tv/wp-content/ql-cache/quicklatex.com-81cc6b6b2ed6639fb705d29bf20983b7_l3.png)
Explanation:
From the question we are told that
The wavelength of the spherical wave is![Rendered by QuickLaTeX.com \lambda = 2.0 \ mm = \frac{2}{1000} = 0.002 \ m](https://documen.tv/wp-content/ql-cache/quicklatex.com-d42e74eb11555998737b499293ca1c8d_l3.png)
The first radius is![Rendered by QuickLaTeX.com r_1 = 4.0 \ mm = \frac{4}{1000} = 0.004 \ m](https://documen.tv/wp-content/ql-cache/quicklatex.com-5e27e58251c2f2d4a081655a98fe6c25_l3.png)
The phase at that instant is![Rendered by QuickLaTeX.com \phi _1 = \pi \ rad](https://documen.tv/wp-content/ql-cache/quicklatex.com-9bb5a238e14f583144247603a541faad_l3.png)
The second radius is![Rendered by QuickLaTeX.com r_2 = 3.5 \ mm = \frac{3.5}{1000} = 0.0035 \ m](https://documen.tv/wp-content/ql-cache/quicklatex.com-d0e1a9e51e389cb4a306d19a75cbf60e_l3.png)
Generally the phase difference is mathematically represented as
this can also be expressed as
So we have that
substituting values