← Wave speed and boundary behaviors

Predict the amount of diffraction

Two harbors face the same sea swell. One has a wide opening, and the water inside stays nearly calm except along the straight-through line. The other has a narrow opening, and waves sweep the whole basin.

Same waves, different gaps. What sets how much a wave spreads when it passes an opening?

Compare the gap's width to the wavelength. That comparison decides the spreading.

A gap many wavelengths wide barely spreads the wave. Most of each front passes through unchanged, and only the ends curl.

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A gap five wavelengths wide: little spreading, only the ends curl.

Narrow the gap, and the spreading grows.

Spreading is greatest when the gap is about one wavelength wide. Beyond such a gap, the fronts fan out in near-semicircles.
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A gap about one wavelength wide: the fronts fan out in near-semicircles.

The wavelength is the yardstick. The same gap spreads long waves more than short ones, because against a longer wavelength the same gap counts as narrow.

So two changes both increase diffraction: a narrower gap, or a longer wavelength. Each brings the gap closer to one wavelength wide.

Gap width against wavelengththe gap isthe spreading ismany wavelengths widesmall: only the ends curla few wavelengths widenoticeableabout one wavelength widegreatest: near-semicircles
Count the gap in wavelengths; the count sets the spread.

A harbor's opening is rebuilt at half its old width. The incoming swell is unchanged. What happens to the spreading of the waves inside?

The wavelength is unchanged, and the gap is now narrower.

A narrower gap sits closer to one wavelength wide, and spreading grows as the gap nears one wavelength.

The waves inside spread more than before.

Two wave trains pass through the same gap, one with short waves and one with long waves. Which spreads more beyond the gap?

The gap is the same for both, so compare it to each wavelength.

Against the longer wavelength, the gap counts as narrower.

The long waves spread more, because the gap is closer to one of their wavelengths wide.

A gap between two ripple-tank barriers is made narrower. The ripples are unchanged. What happens to the spreading beyond the gap?

When is the spreading of a wave through a gap greatest?

Hale says: 'Through the same gap, waves with a longer wavelength spread more than waves with a shorter wavelength.' Is Hale correct?

Your turn

Straight ripples with 2 cm wavelength meet two openings: one 3 cm wide and one 20 cm wide. Which statement compares the spreading beyond them?

A harbor's opening is many wavelengths wide. What do the waves beyond the opening look like?

In a ripple tank, the dipper is slowed, making the ripples' wavelength longer. The gap in the barrier is unchanged. What happens to the spreading beyond the gap?