Physics
Frequency Spectrum
Quick fact
When sunlight passes through a prism, the rainbow you see is actually the frequency spectrum of visible light—and beyond both ends lie invisible infrared and ultraviolet frequencies.
Why this is interesting
If you press a single key on a piano, you hear a pure tone—but when you listen to a chord, how does your ear separate the notes? The answer lies in the frequency spectrum, a hidden map of every sound's ingredients.
Read the full explanation
Understanding Frequency Spectrum
Imagine a complex sound like a crashing wave or a spoken word. At first glance, it looks like a messy squiggle on an oscilloscope. But this shape is actually the sum of many simpler waves, each with its own frequency (how fast it oscillates) and amplitude (how strong it is). The frequency spectrum is a way to unpack that mix: it shows a graph where the horizontal axis is frequency (from low to high) and the vertical axis is amplitude. Each spike in the graph represents a pure tone present in the original signal. For example, a musical note from a guitar contains a fundamental frequency plus quieter higher frequencies called harmonics. The spectrum reveals exactly which harmonics are there and how loud each one is.
A deeper explanation
The mathematical tool that extracts the frequency spectrum from a time-varying signal is the Fourier transform. It works by comparing the signal to many sine waves of different frequencies and measuring how much each sine wave contributes. This process converts the signal from the time domain (amplitude vs. time) into the frequency domain (amplitude vs. frequency). Why does this matter? Because many systems—like radio receivers, MRI machines, and audio equalizers—operate more naturally in the frequency domain. For instance, a radio station transmits at a specific carrier frequency; your receiver tunes to that exact frequency to pick up the signal. In medicine, MRI uses radio frequency pulses to excite hydrogen atoms and then analyzes the frequency spectrum of the emitted signals to construct images. Even our ears perform a real-time frequency analysis on the cochlea’s basilar membrane, which is why we can distinguish between a flute and a trumpet playing the same note—they have different harmonic spectra.