INTERFERENCE & DIFFRACTION

1.

A phase synchronized linear array of 6 radiotelescopes 40 km apart operates on a wavelength of 25 cm.

(a)

What angular separation of distant sources can it resolve? Please give your answer in arc seconds.

(b)

If it ``looks at'' a source 800 light years away, what is the source linear resolution compared to the Sun-Jupiter distance?

2.

A sound absorbing straight wall is 20 m high and 100 m long; at its centre, ground level, is a 1.2 m wide open doorway. You are 32 m straight in front of the doorway when a whistle 55 m directly behind the doorway begins to blow at 900 Hz. How far along a line parallel to the wall (and passing through your present position) must you move before the sound first becomes imperceptible?

3.

Consider a series of 10 equal slits, each 0.004 cm wide, arrayed in a straight line with equal spacing so that 0.22 cm separates the centres of the first and last slits. This configuration is illuminated from behind by a distant source of light of wavelength 0.546 micron [$\mu$m].

(a)

How many major intensity peaks will you see in the entire pattern displayed on a wide screen 20 m away before the pattern first fades away laterally?

(b)

How far apart and how wide (in mm) are the principal maxima near the centre of the screen? [``principal'' $\equiv$ ``major'']

4.

It is claimed that a satellite carries a camera capable of discerning details as small as 12 cm across at a distance of 200 km, using visible light of wavelength 0.55 $\mu$m. What must be the minimum diameter of the camera lens?

5.

Two loudspeakers 60 cm apart each emit 40 watts of 1800 Hz sound uniformly over a conical region representing 1/9 of the full sphere of possible directions. Imagine a line AB parallel to the line joining the speakers, but 28 m distant from the speakers. Then suppose that you are 4 m off the system's symmetry axis (bisecting the line joining the speakers) on line AB.

(a)

If only one speaker is operating, what is the sound intensity (in watts/m²) at your location?

(b)

If both speakers are on, and in phase, what sound intensity do you receive?