Your roommate studying biology mentions that dolphin hearing is rather strange, as the dolphin’s…

Your roommate studying biology mentions that dolphin hearing is rather strange, as the dolphin’s ear is inside its jaw. With sound emitted and partly focused forward by the dolphin’s interior “melon”, exiting spherical waves reflect off distant objects and return as planar acoustic waves, which somehow reach the dolphin’s inner ear. Your roommate professes that there have been several different ideas about dolphin hearing in the past. Some literature suggests that the dolphin’s teeth act as acoustic antennas, others sources mention a trumpet-like shape of “acoustic fat” which channels the sonar radiation towards the ear and one text describes that the varying density of “acoustic fat” may provide a focusing effect to curve refracted acoustic rays. Guided by your PHS 1001 conceptual knowledge, you explain that the shape of the dolphin’s head alone could guide acoustic rays to the inner ear, if interior bones and other bits can be ignored. To prove your point, you try to demonstrate this using a laser pointer and your roommate’s glass model of the dolphin head but the experiment is not clear. Instead you draw a diagram and closely approximate the toy dolphin’s nose/jaw as a cone, placing the inner ear on the optic axis (dotted line), with three incident parallel rays striking the dolphin’s cone-like nose; ray!, ray2 and ray3. The initial diagram is shown below.

Melon y

ray,

ray3 Ys T CD Ear ray2 Closed mouth jaw

dear

Figure 1: model of the toy dolphin head (not to scale).

You have drawn the slope of the jaw to make an angle with respect to the horizontal of Oi = 20°. The angle between rayi and the jaw is also 01 = 20°. The refractive index in air is taken to be 1.00 and that of the glass is ng = 1.55. The horizontal distance of the tail of rayi from the ear is dear = 2cm. The constant vertical height of rays is yi = 5cm above the optic axis and ray2 is lcm above the horizontal dotted line. Ray3 is exactly mid-way between the other two rays, at a height of 3cm.

(a) Using Snell’s law, find the point at which the refracted rayi intersects the dotted optic axis to state how far this intersection point is from the toy dolphin’s ear (12 marks).

(b) Use Snell’s law again to find where ray2 intersects the optic axis and state how far this point is from the toy dolphin’s ear (6 marks).

(c) Without using Snell’s law or any angle, find where ray3 intersects the optic axis with respect to the intersection points of rayi and ray2 (6 marks).

(d) In two sentences, state what the toy dolphin does to parallel rays that are incident upon the straight jaw cone, including rays from the lower part of the jaw (8 marks).

(e) In one sentence, state what the effect of the spherical end at the closed mouth does to parallel rays; do not include numbers or any formula in your answer (4 marks).

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