TwiddleLab / Physics / Waves and Sound

Waves Add Up: Interference

Lesson 6 of 10 · 7 min · Free, no account needed

What you will learn

• Superposition: where waves overlap, their heights add. Afterwards each one carries on unchanged.
• Constructive interference: crest on crest makes a bigger wave.
• Destructive interference: crest on trough cancels. Noise-cancelling headphones play an anti-wave.

Start the lesson

How the lesson goes

1. Noise-cancelling headphones make silence by playing more sound. How? Start with a rope.

   A hump and an equal dip run towards each other.

2. Run it. What happens where they overlap?

   Dashed lines show each pulse on its own. The rope is the bold line.

3. Two steady waves. Slide one and watch their sum.

4. The words for adding waves.

   Superposition: where waves overlap, the heights add up (a dip counts as negative). Then each wave carries on as before.

   Constructive interference: crests meet crests, the result is bigger.

   Destructive interference: crests meet troughs, they cancel. Equal and opposite waves give silence.

   Simplified: ideal waves that add exactly. Real headphones cancel low steady hums well, sudden high sounds less well.

5. Game: Cancel the noise. Leave less than 10 % of each hum.

   Slide your anti-wave and set its height, then Lock in.

6. Two speakers make ripples in a tank. Find the calm spots.

   At a calm spot the distance to one source is half a wavelength longer (or 1.5, 2.5...) than to the other, so one ripple's crest always arrives with the other's trough.

7. Math: add two waves point by point. Which pair cancels?

   Shift a wave by half its length and every crest lands where a trough was: the shifted wave is the original flipped upside down, so the sum is zero everywhere.

8. The headphone's anti-wave arrives half a period late. What do you hear?

   An anti-wave is the hum flipped. Delaying a wave by half a period also flips it, so the two flips cancel and it matches the hum: the heights add.

9. Your anti-wave against the plane's hum.

Previous lesson: Echoes: Sonar and Ultrasound · Next lesson: Standing Waves: Why Strings Have Notes · Part of the course: Waves and Sound

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