Frequencies
A visual guide to cycles, waves, and “how often.”

Frequency is just “how often” something repeats.

Sound, radio, Wi-Fi, sunlight, music notes, brainwaves, heartbeats — all of them are patterns over time. Frequency tells you how many cycles happen per second.

Unit
Hertz (Hz)
Meaning
cycles / second
Formula
f = 1 / T
Live idea
Same amplitude, different frequency
Tip: move the slider
to change cycles/sec
Higher Hz = more wiggles in the same time window. Amplitude is “how tall,” frequency is “how often.”

Basics

A wave is a repeating pattern. Frequency describes repetition speed; period describes the time for one cycle. Lots of “frequency” talk becomes easy once you can swap between Hz ↔ period ↔ wavelength.

Frequency
f (Hz)

How many cycles happen each second.

Period
T (seconds)

Time for one cycle. Relationship: f = 1/T.

Wavelength
λ (meters)

Distance per cycle. If a wave travels at speed v, then v = f·λ.

Examples of “1 Hz”
  • • One blink per second
  • • A metronome tick each second
  • • A slow pendulum swing
Examples of “10 Hz”
  • • Rapid vibration you can see
  • • Low-frequency rumble in audio
  • • A fast strobe effect
Examples of “1,000 Hz”
  • • A high-ish tone (1 kHz)
  • • Many electronic beeps
  • • Phone/alert-style signals

Sound frequencies

Humans typically hear roughly 20 Hz to 20,000 Hz (20 kHz). Lower frequencies feel like thumps/rumble; higher frequencies feel like hiss/brightness.

Musical reference: A4 = 440 Hz
Audio bands (rough intuition)
Sub-bass20–60 Hz
Bass60–250 Hz
Mids250–2,000 Hz
Presence2–6 kHz
Brilliance / “air”6–20 kHz

These ranges vary by source, but the “feel” of them is widely used in mixing and audio engineering.

Loudness is not frequency

Loudness relates to amplitude, often measured using decibels (dB). Frequency is “how often.” You can have:

  • • A very low, very loud bass boom (low Hz, high amplitude)
  • • A very high, very quiet hiss (high Hz, low amplitude)
Resonance
When a system “likes” a frequency

Push a swing at the right timing and it grows. In audio, resonance can make certain notes jump out.

Electromagnetic spectrum

Light is also a wave — just at wildly higher frequencies than sound. Visible light is roughly in the hundreds of terahertz (THz).

Radio

kHz → GHz. Communication, broadcasting, Wi-Fi, cellular.

~ 10³ – 10⁹ Hz
Microwave / Infrared

Higher than radio. Heat radiation sits in infrared.

~ 10⁹ – 10¹⁴ Hz
Visible → UV → X-ray

Visible light is a narrow slice. UV and beyond carry more energy.

~ 4×10¹⁴ Hz and up
Energy and frequency

In quantum terms, higher-frequency light has higher energy per photon (that’s why UV can cause sunburn). Different parts of the spectrum interact with matter in different ways — which is why we use different bands for different tech.

Sampling & digital frequency

In computers, we “sample” a continuous wave at fixed intervals. The sample rate is measured in Hz too (samples per second). More samples per second can represent higher frequencies.

Nyquist idea (the simple version)

To capture a frequency, your sample rate must be more than that frequency. Example: 44,100 Hz audio can represent up to about 22,050 Hz.

CD Audio
44,100 Hz
Max captured
~22,050 Hz
Aliasing (when frequencies “fold”)

If you try to sample a frequency higher than half the sample rate, it can appear as a different, lower frequency. That’s why anti-alias filters exist.

Think of it like filming a spinning wheel: at some speeds it looks like it slows down or reverses.

Quick tools

Convert between frequency and period, find wavelengths, and get “what does this feel like?” ranges.

Hz ↔ Period
f = 1/T
Period
0.5 s

If f is 0, period is “infinite” (it’s not repeating).

Wavelength
λ = v / f
343 m/s ≈ speed of sound in air (room temp)
Wavelength
0.780 m
“What range is this?”

Type a frequency and get a quick label (sound bands + EM hints).

Result
Midrange sound (speech clarity zone)
Also: far below visible light.
This is an intuition helper, not a lab-grade classifier.

Interactive playground

Make a wave. Change frequency, amplitude, and phase. Watch the “wiggles” compress and expand.

Blue = waveform. Grid shows time slices across the window.
5 Hz
1.0
0°
1.5 s
Brainwave bands (popular labels)
  • • Delta: ~0.5–4 Hz
  • • Theta: ~4–8 Hz
  • • Alpha: ~8–12 Hz
  • • Beta: ~12–30 Hz
  • • Gamma: ~30–100+ Hz

These are conventional ranges used in EEG discussions.

Music notes (equal temperament)

Notes double every octave: 220 Hz → 440 Hz → 880 Hz. That “doubling” is why pitch feels logarithmic.

Example
A3 = 220 Hz, A4 = 440 Hz, A5 = 880 Hz
Vibration everywhere

Springs, bridges, glass, engines, guitar strings — everything has “natural” frequencies. Engineering often means avoiding unwanted resonance.

If you remember one thing: frequency is “how often,” not “how loud.”