Microwaves have frequencies in the range 10^9 to 10^12 / s (cycles per second), equivalent to be

step 1 In order to find the wavelength, we'll divide the speed of light by the given frequency of the m

Microwaves have frequencies in the range 10^9 to 10^12 / s...

Microwaves have frequencies in the range $10^{9}$ to $10^{12} / \mathrm{s}$ (cycles per second), equivalent to between 1 gigahertz and 1 terahertz. What is the wavelength of microwave radiation whose frequency is $1.258 \times 10^{10} / \mathrm{s}$ ?

Key Concepts

Speed of Light

The speed of light, typically denoted as c, is a universal constant approximately equal to 3.00 × 10^8 meters per second in a vacuum. This constant is pivotal in the relationship between frequency and wavelength, serving as the scaling factor that connects these two quantities in electromagnetic wave propagation.

Scientific Notation

Scientific notation is a method of expressing very large or very small numbers in a compact form using powers of ten. It is especially useful in physics and engineering when dealing with the extreme ranges of values, such as the frequencies and wavelengths encountered in the study of electromagnetic radiation.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which are classified by their wavelength and frequency. Microwaves fall within a specific range of this spectrum, characterized by relatively long wavelengths compared to infrared, visible, or ultraviolet light. Understanding where microwaves are placed on the spectrum helps in grasping their interaction with matter and their common applications in communication and heating technologies.

Frequency and Wavelength Relationship

A fundamental concept in the study of waves is the inverse relationship between frequency and wavelength, expressed by the equation ? = c/f, where ? is the wavelength, c is the speed of light, and f is the frequency. This relationship explains how higher frequency waves have shorter wavelengths and vice versa, providing a critical tool for analyzing and calculating properties of electromagnetic radiation.

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