A cellular phone is actually a radio transmitter and receiver. You receive an incoming call in the form of a radio wave of frequency \(880.65 \mathrm{MHz}\). What is the wavelength (in meters) of this wave?

When discussing radio waves, it's essential to understand the concept of frequency. Frequency is the number of times a wave repeats itself within a second and is measured in units called Hertz (Hz). Radio waves are a type of electromagnetic radiation and their frequencies are situated on the electromagnetic spectrum's lower end.

For instance, in the exercise provided, a cellular phone receives a call through a radio wave with a frequency of 880.65 megahertz (MHz). The 'mega' prefix means 'million', indicating that the wave's frequency is 880.65 million cycles per second. This frequency determines the pitch or tone we perceive and is crucial for communication technologies, enabling different devices to operate without interfering with one another.

Hertz (Hz) is a unit that measures frequency, named after the physicist Heinrich Hertz. Conversion to and from Hertz is a key skill in understanding and applying electromagnetic wave principles. Typically, frequency is provided in different magnitudes, utilizing prefixes such as kilohertz (kHz), megahertz (MHz), and gigahertz (GHz), among others. One MHz is equal to one million Hertz.

As seen in the exercise, converting MHz to Hz involves simply multiplying by the factor of a million, or mathematically, by 10^6. This aids in simplifying calculations and aligns the frequency unit with the commonly used speed of light in meters per second (m/s). Hertz conversion is fundamental when dealing with the frequency of waves, as it allows for accurate and consistent computation of wavelength or energy.

The speed of light is a fundamental constant in the realm of physics, denoted by the symbol \(c\). It is the speed at which all light waves, including radio waves, travel through the vacuum of space. The universally agreed upon value of the speed of light is approximately \(3 \times 10^8\) meters per second (m/s).

Understanding the speed of light is crucial when calculating the wavelengths of various frequencies. As radio waves are a form of light, they too travel at this universal speed. In our exercise, we use the speed of light to determine the length of one full wave cycle, or wavelength, given the wave's frequency. The relationship between light's speed, frequency, and wavelength is interdependent—a change in one variable will affect the others, demonstrating the intertwined nature of these fundamental properties of waves.