Calculate the frequency of an EM wave with a wavelength the size of (a) the thickness of a piece of paper \((60 \mu \mathrm{m}),(\mathrm{b})\) a \(91-\mathrm{m}\) -long soccer field, (c) the diameter of Earth, (d) the distance from Earth to the Sun.

Short Answer

Expert verified
Question: Calculate the frequency of electromagnetic waves for the following wavelengths: (a) the thickness of a piece of paper (60 µm), (b) the length of a soccer field (91 meters), (c) the diameter of Earth (12,742 km), and (d) the distance from Earth to the Sun (149.6 million km). Answer: (a) The frequency of the EM wave with a wavelength equal to the thickness of a piece of paper is approximately 5 * 10^12 Hz. (b) The frequency of the EM wave with a wavelength equal to the length of a soccer field is approximately 3.3 * 10^6 Hz. (c) The frequency of the EM wave with a wavelength equal to the diameter of Earth is approximately 23.6 Hz. (d) The frequency of the EM wave with a wavelength equal to the distance from Earth to the Sun is approximately 2 * 10^(-6) Hz.

Step by step solution

01

Problem 1 - Thickness of a piece of paper; 60 µm

The thickness of the paper is given as 60 micrometers (µm). We need to first convert the micrometers into meters: 60 µm = 60 * 10^(-6) meters Now, we'll calculate the frequency using the formula we derived before: f = c / λ f = (3 * 10^8) / (60 * 10^(-6)) f ≈ 5 * 10^12 Hz So, the frequency of the EM wave with a wavelength equal to the thickness of a piece of paper is approximately 5 * 10^12 Hz.
02

Problem 2 - 91-meter long soccer field

The wavelength of the EM wave is given as the length of a soccer field, which is 91 meters. We'll use our formula to calculate the frequency: f = c / λ f = (3 * 10^8) / 91 f ≈ 3.3 * 10^6 Hz The frequency of the EM wave with a wavelength equal to the length of a soccer field is approximately 3.3 * 10^6 Hz.
03

Problem 3 - Diameter of Earth

For this problem, the wavelength of the EM wave is the diameter of Earth, which is approximately 12,742 kilometers. Before using the formula, we need to convert kilometers to meters: 12,742 km = 12,742,000 meters Now we can calculate the frequency: f = c / λ f = (3 * 10^8) / (12,742,000) f ≈ 23.6 Hz The frequency of the EM wave with a wavelength equal to the diameter of Earth is approximately 23.6 Hz.
04

Problem 4 - Distance from Earth to the Sun

In this case, the wavelength of the EM wave is equal to the average distance from Earth to the Sun, which is approximately 149.6 million kilometers. We will convert it to meters first: 149,600,000 km = 149,600,000,000 meters Now, we can calculate the frequency: f = c / λ f = (3 * 10^8) / (149,600,000,000) f ≈ 2 * 10^(-6) Hz The frequency of the EM wave with a wavelength equal to the distance from Earth to the Sun is approximately 2 * 10^(-6) Hz.

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