Harbor seals, like many animals, determine the direction from which a sound is coming by sensing the difference in arrival times at their two ears. A small difference in arrival times means that the object is in front of the seal; a larger difference means it is to the left or right. There is a minimum time difference that a seal can sense, and this leads to a limitation on a seal's direction sense. Seals can distinguish between two sounds that come from directions 3∘ apart in air, but this increases to 9∘ in water. Explain why you would expect a seal's directional discrimination to be worse in water than in air.

that the angle must be increased to maintain the minimum time of discrimination due to the increase in the speed of sound in material

Explanation:

The direction of sound is detected by the difference in time of reception of each ear, the speed of the wave is

             v = d / t

             t = d / v

In air the velocity is v = 330 m / s, let's use trigonometry

           Cos 3 = d / L

           L = d / cos 3

The difference in distance is

            Δd = d - d / cos 3 = d (1- 1 / cos3)

             t = Δd / 330

When the animal is in the water the speed of sound is

              v = 1540 m / s

So time is

             t' = Δd ’/ 1540

            t ’= Dd’ / 4.67  330

So if  t = t’  is the minimum response time, the distance must be increased

            Δd ’= 4.6 Δd

            1-1 / cos θ = 4.6 (1- 1 / cos 3) = -4.6 0.00137 = -0.00631

           1 + 0.0063 = 1 / cos θ

           1.00631 = 1 / cos θ

           Cos θ = 1 / 1.00631

           Tea = 6.5

We see that the angle must be increased to maintain the minimum time of discrimination due to the increase in the speed of sound in material