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with a cooking dish in a fixed position, the antinodes can appear as burn marks

ID: 2071468 • Letter: W

Question

with a cooking dish in a fixed position, the antinodes can appear as burn marks on foods such as carrot strips or cheese. The separation distance between the burns is measured to be 6.00 cm. Calculate the speed of the microwaves from these data. Consider a bright star in our night sky. Assume its distance from the Earth is 20.0 light-years (ly) and its power output is 4.00 times 1028 W, about 100 times that of the Sun. Find the intensity of the starlight at the Earth. Find the power of the starlight the Earth intercepts. One light-year is the distance traveled by light through a vacuum in one year. What are the wavelengths of electromagnetic waves in free space that have frequencies of 5.00 times 1019 Hz and 4.00 times 109 Hz?

Explanation / Answer

(a) distance = 20 ly = 20 * 3x10^8 * 3.156x10^7 = 1.893 x 10^17 meters

intensity = P /4pi r^2 =

               = 100x10^28 / 4 * pi * (1.893x10^17)^2 =

               = 2.22 x 10^-6 W/m^2

(b) power intercepts = intensity * pi r^2 = 2.22 x 10^-6 * pi * 6380000^2 =

             = 2.84 x 10^8 Watts