General Wave Properties: Question 9

Syllabus 3.1

Multiple choice Extended 1 mark

Ocean swell waves with a wavelength of $12\text{ m}$ approach the entrance to a small harbour. The width of the gap between the two harbour walls can be altered. Which gap width would cause the incoming swell to diffract most strongly, spreading out widely once inside the harbour?

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Step 1: Recall the condition for strong diffraction

A wave diffracts most strongly when the width of the gap it passes through is about the same size as its wavelength. If the gap is much wider or much narrower than the wavelength, the wave spreads out far less.

Step 2: Compare each option with the wavelength

The swell’s wavelength is $\lambda = 12\text{ m}$ . Compare each gap width with this value:

Gap width	Compared with $\lambda = 12\text{ m}$
$1.2\text{ m}$	$10\times$ smaller than the wavelength
$12\text{ m}$	equal to the wavelength
$120\text{ m}$	$10\times$ larger than the wavelength
$1200\text{ m}$	$100\times$ larger than the wavelength

Step 3: Select the gap width closest to the wavelength

Only the $12\text{ m}$ gap matches the condition (gap width $\approx$ wavelength), so this gap width causes the strongest diffraction.

Final answers

Gap width for strongest diffraction $= \boxed{12\text{ m}}$ , option B