Alone in the Dark

You're in a dark, soundproof house at night. The roof is 7 m high, and has a long straight crack in it which is only 0.05 mm wide. Apart from the crack, the walls of the house do not let in any light or sound.

(a)

A bright star at 90 degrees above the horizon, see Fig. 4, emits light of wavelength $\lambda=500$ nm. Where in the room should you stand to be able to see the star? Give your answer in terms of the horizontal distance $x$ between your eye and the crack. Assume you're 2 m tall.

HINT: You can assume that you do not see anything once you're outside the central intensity maximum of the diffraction pattern. You should be able to invent a sensible definition of the width of that maximum.

(b)

If an airplane passes above the house, where in the room should you stand to be able to hear it? You can assume that the sound produced by the airplane has frequency $f=100$ Hz, and the speed of sound in air is 330 m/sec.

(c)

What is the crucial difference between light and sound that makes the answers to (a) and (b) so different?

Figure: The dark house with a crack in the roof.