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ScientistGrades 11–12⏱ 20 min

Wave interference

Make ripples from two sources and find where the waves add up and where they cancel, using the path difference.

Standards: HS-PS4-1

1Wonder

Noise-cancelling headphones play extra sound, and the room gets quieter. How can adding a sound make less noise?

2Explore

Ripple tank

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Turn your phone sideways, or open this lesson on a tablet or computer. The explanation and quiz below work here.

S₁S₂d₁ = 18 cmd₂ = 19.1 cmd₁ − d₂ = −1 cm = −0.51 λCrest meets trough: still watermotion at the probeSillyChili
Try this
  • Turn off the second source. Then turn it back on. What new pattern appears?
  • Drag the probe to a calm spot. What is d₁ − d₂ there, in wavelengths?
  • Now find a spot where the water moves a lot. What is d₁ − d₂ there?
  • Turn on Show the still lines. What happens to them when you move the sources apart? When you make λ longer?

3Explain

+=SillyChili
Step 1 of 5

Waves add up

When two waves meet, the water height is the sum of the two. A crest plus a crest makes a crest twice as tall. This is constructive interference.

Interferenced1−d2=m λadd upd1−d2=(m+12)λcancel\begin{aligned} d_1 - d_2 &= m\,\lambda &&\text{add up} \\ d_1 - d_2 &= \left(m + \tfrac12\right)\lambda &&\text{cancel} \end{aligned}

When waves overlap, their heights add. Whether they add up or cancel depends on the path difference measured in wavelengths.

4Practice

Question 1 of 5

A crest 3 cm high meets another crest 3 cm high. How high is the water there?

cm

5Recap

  • Where waves overlap, their heights add.
  • Crest + crest → bigger wave (constructive); crest + trough → cancel (destructive).
  • Path difference mλ → add up; (m + ½)λ → cancel.
  • Two sources make a pattern of busy and still lines.