Spectrogram Waterfall Display
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About This MicroSim
A single spectrum is a snapshot. A spectrogram is what you get by stacking those snapshots side by side as time passes, so you can see how the frequency content changes.
Three axes on a two-dimensional screen:
- Vertical — frequency, low at the bottom
- Horizontal — time, newest at the right
- Color — magnitude, dark for quiet through blue, cyan, and yellow to white for loud
Each column is one processed frame. The display scrolls left as new frames arrive, exactly as it would on a real analyzer.
Learning to Read It
Every sound has a visual signature, and once you know a few you can read a spectrogram at a glance:
| Sound | Signature |
|---|---|
| Rising whistle | A bright line sloping upward |
| Falling whistle | A bright line sloping downward |
| Two-tone chord | Two parallel horizontal lines |
| Clap | A single vertical stripe spanning all frequencies |
The clap is the most instructive one. A sharp transient is not a frequency — it is all frequencies at once, briefly. That is why it appears as a vertical stripe rather than a horizontal line, and it is the time-frequency dual of the tone.
The Uncertainty Underneath
Look at how the whistle's line has thickness rather than being infinitely thin. That thickness is your frequency resolution, set by the frame size.
Make frames longer and the line gets thinner — but each column now covers more time, so a fast sweep smears horizontally instead. Make frames shorter and you track time precisely but frequency blurs.
You cannot have both. This is the time-frequency uncertainty principle, and a spectrogram is where it becomes something you can see rather than a theorem.
How to Use
- Select Rising whistle and press Play. Watch the bright trace climb.
- Switch to Falling whistle and confirm the mirror image.
- Select Two-tone chord. Two steady horizontal lines — the pitches are not changing, so the traces do not move.
- Select Silence then a clap. Nothing, then one vertical stripe across the whole frequency range, fading over a few frames.
- Compare the chord and the clap. One is narrow in frequency and wide in time; the other is the exact opposite.
Lesson Plan
Grade Level
Undergraduate (college junior/senior)
Duration
10-12 minutes
Prerequisites
- A spectrum is a magnitude per frequency bin
- Frames and hop size
Learning Objective
Students will be able to examine a scrolling waterfall spectrogram and interpret how a changing pitch appears as a moving colored trace over time.
Activities
- Match signatures (4 min): Students view all four examples and sketch each signature from memory afterward.
- Explain the clap (4 min): Students explain why a transient appears as a vertical stripe rather than a horizontal line.
- Predict (4 min): Students describe what a siren, a hand clap in a reverberant room, and a sustained hum would each look like.
Assessment
Ask: "You see a spectrogram with a bright horizontal line at 440 Hz and faint parallel lines at 880 and 1320 Hz. What is the sound, and what are the faint lines?"
Related Resources
References
- Spectrogram — the display type and its conventions.
- Short-time Fourier transform — how the columns are produced.
- Time-frequency uncertainty — the resolution tradeoff visible in the trace thickness.