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Chapter 22: Problem 13

What is the frequency of the microwaves in a microwave oven? The wavelength is \(12 \mathrm{cm}\)

Short Answer

Expert verified
Answer: The frequency of the microwaves is 2.5 × 10^9 Hz.

Step by step solution

01

Identify the relevant formula

We know that the speed of light (\(c\)) is related to the frequency (\(f\)) and wavelength (\(\lambda\)) using the formula \[ c = f \lambda \]
02

Convert the wavelength to meters

The given wavelength is in centimeters, so we need to convert it to meters: \[ 12\,\mathrm{cm} = 0.12\,\mathrm{m} \]
03

Find the speed of light

The speed of light (\(c\)) is a constant, and it is approximately equal to \(3.0 \times 10^8 \mathrm{m/s}\).
04

Solve the equation for frequency

Now we'll use the formula \(c = f \lambda\) and substitute the known values, which will allow us to find the frequency (\(f\)) of the microwaves. \[ 3.0 \times 10^8\,\mathrm{m/s} = f (0.12\,\mathrm{m}) \]
05

Calculate the frequency

Divide both sides of the equation by \(0.12\,\mathrm{m}\) to solve for \(f\): \[ f = \dfrac{3.0 \times 10^8\,\mathrm{m/s}}{0.12\,\mathrm{m}} = 2.5 \times 10^9\,\mathrm{Hz} \] The frequency of the microwaves in a microwave oven is \(2.5 \times 10^9\,\mathrm{Hz}\).

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Most popular questions from this chapter

The index of refraction of water is \(1.33 .\) (a) What is the speed of light in water? (b) What is the wavelength in water of a light wave with a vacuum wavelength of \(515 \mathrm{nm} ?\)
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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.
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