Math LabLab i Waves

Lab i

See a sound

Sound is a wiggle in the air. Here you can watch the wiggle while you hear it — and even see your own voice.

the oscilloscope — a camera for sound

frequency — wiggles per second440 HzA4

one wiggle takes T = 1 ÷ 440 = 2.27 ms

volume — height of the wiggle60%

Sound is a wiggle

When something makes a sound, it shakes the air back and forth — like a tiny push-pull, over and over. The line on the screen is a drawing of that shaking.

Frequency = wiggles per second

440 Hz means 440 wiggles every second. More wiggles per second sounds higher. Fewer sounds lower. That's the whole secret of pitch.

T = 1 ÷ f

If there are 440 wiggles in one second, each wiggle gets 1÷440 of a second — about 2.3 milliseconds. Faster wiggles, shorter turns. Watch the number update as you slide.

For the classroom

Learning goals

  • Sound is a vibration; the oscilloscope turns an invisible vibration into a visible graph.
  • Frequency (Hz) counts cycles per second and maps directly to musical pitch.
  • Period and frequency are reciprocals: T = 1/f — a first, concrete meeting with an inverse relationship.

Try this

  1. 1.Set 200 Hz, then 400 Hz, then 800 Hz. Ask: what happens to the wiggles on screen each time we double? (They squeeze together — and the note jumps an octave.)
  2. 2.Turn on the microphone and have three students hum the same note. Compare the tidiness of their lines — then have one hum higher and ask the class to spot whose wave got narrower.