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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 脳 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

Two identical television signals are sent between two cities that are \(400.0 \mathrm{km}\) apart. One signal is sent through the air, and the other signal is sent through a fiber optic network. The signals are sent at the same time but the one traveling through air arrives \(7.7 \times 10^{-4}\) s before the one traveling through the glass fiber. What is the index of refraction of the glass fiber?
How long does it take light to travel from this text to your eyes? Assume a distance of \(50.0 \mathrm{cm}\).
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?
The radio telescope in Arecibo, Puerto Rico, has a diameter of $305 \mathrm{m}$. It can detect radio waves from space with intensities as small as \(10^{-26} \mathrm{W} / \mathrm{m}^{2} .\) (a) What is the average power incident on the telescope due to a wave at normal incidence with intensity \(1.0 \times 10^{-26} \mathrm{W} / \mathrm{m}^{2} ?\) (b) What is the average power incident on Earth's surface? (c) What are the rms electric and magnetic fields?

You and a friend are sitting in the outfield bleachers of a major league baseball park, 140 m from home plate on a day when the temperature is \(20^{\circ} \mathrm{C}\). Your friend is listening to the radio commentary with headphones while watching. The broadcast network has a microphone located \(17 \mathrm{m}\) from home plate to pick up the sound as the bat hits the ball. This sound is transferred as an EM wave a distance of \(75,000 \mathrm{km}\) by satellite from the ball park to the radio. (a) When the batter hits a hard line drive, who will hear the "crack" of the bat first, you or your friend, and what is the shortest time interval between the bat hitting the ball and one of you hearing the sound? (b) How much later does the other person hear the sound?
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