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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

Light of wavelength \(659.6 \mathrm{nm}\) is emitted by a star. The wavelength of this light as measured on Earth is \(661.1 \mathrm{nm} .\) How fast is the star moving with respect to Earth? Is it moving toward Earth or away from it?
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.
The magnetic field in a microwave traveling through vacuum has amplitude $4.00 \times 10^{-11} \mathrm{T}\( and frequency \)120 \mathrm{GHz}$. Find the amplitude and frequency of the electric field.
A magnetic dipole antenna is used to detect an electromagnetic wave. The antenna is a coil of 50 turns with radius \(5.0 \mathrm{cm} .\) The EM wave has frequency \(870 \mathrm{kHz}\) electric field amplitude $0.50 \mathrm{V} / \mathrm{m},\( and magnetic field amplitude \)1.7 \times 10^{-9} \mathrm{T} .$ (a) For best results, should the axis of the coil be aligned with the electric field of the wave, or with the magnetic field, or with the direction of propagation of the wave? (b) Assuming it is aligned correctly, what is the amplitude of the induced emf in the coil? (Since the wavelength of this wave is much larger than \(5.0 \mathrm{cm},\) it can be assumed that at any instant the fields are uniform within the coil.) (c) What is the amplitude of the emf induced in an electric dipole antenna of length \(5.0 \mathrm{cm}\) aligned with the electric field of the wave?
A polarized beam of light has intensity \(I_{0} .\) We want to rotate the direction of polarization by \(90.0^{\circ}\) using polarizing sheets. (a) Explain why we must use at least two sheets. (b) What is the transmitted intensity if we use two sheets, each of which rotates the direction of polarization by \(45.0^{\circ} ?\) (c) What is the transmitted intensity if we use four sheets, each of which rotates the direction of polarization by \(22.5^{\circ} ?\)
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