A student sets up a ripple tank experiment to compare the diffraction of waves through gaps of different widths. She uses a motor to generate plane waves an...

(a)

• As the ratio of gap width to wavelength increases, the amount of diffraction decreases. [1]
• The most diffraction occurs when the ratio is close to 1 or less (gap width equal to or smaller than the wavelength). [1]

The table shows this trend clearly: at a ratio of 0.5, the wavefronts are almost fully circular (maximum spreading), while at a ratio of 8.0, there is very little spreading. Diffraction is strongest when the gap is comparable to the wavelength.

(b) The most effective diffraction (fully circular wavefronts) occurs at a gap/wavelength ratio of 0.5 (or 1.0). [1]

At ratio 0.5 the gap is smaller than the wavelength, forcing the waves to spread in all directions as if the gap were a point source.

(c) She could increase the depth of the water in the tank. [1]

Water waves travel faster in deeper water. Since the motor keeps the frequency constant, \(v = f\lambda\) means a higher speed produces a longer wavelength.

(d)

\(v = f \times \lambda = 5.0 \times 2.0 = 10\text{ cm/s}\) [1]

(e)

• The wavelength of visible light is extremely small (about \(5 \times 10^{-7}\) m) compared to the width of a window (perhaps 1 m). [1]
• The gap/wavelength ratio is therefore extremely large (around 2 000 000), so there is negligible diffraction and light passes through as a straight beam with sharp shadow edges. [1]

This is exactly the same physics as the 16.0 cm gap in the experiment: when the gap is many times larger than the wavelength, the waves pass through with almost no spreading.

(f) Measure the angle of spread of the diffracted wavefronts (e.g. using a protractor or by photographing the pattern and measuring digitally). [1]

Quantifying the angle allows a numerical comparison between different gap/wavelength ratios, rather than relying on qualitative descriptions.

(g) Mop up any water spills immediately to prevent slipping, or keep electrical connections away from the water. [1]

(h) The sloped edges (beaches) absorb the waves and prevent reflections from the tank walls. [1]

Without beaches, reflected waves would overlap with the incident waves and create a confused interference pattern, making it impossible to observe the diffraction clearly.