## Figure P26

(Unit impulses)

Normalizer dpr = a*b* (p-q)/(b-a) (dprestimates pr over 0 = . = a/2r/ms)

Give the spike responses of the RPFM spike generator for: a. A pulse of pressure: p(t) = Po [U(t) - U(t - 20)]. The pulse is 20 ms in duration; Po = 3 psi. Let a = 2, b = 3 r/ms.

b. A pressure sine wave of varying frequency: p(t) = Po sin(2nf t). Let Po = 3 psi and let 0.05 = f = 5 cycles/ms. Plot the steady-state spike frequency vs. f.

2.7. It is known that the primary response of some animals' photoreceptor cells is hyperpolarization upon illumination, while absorption of light in others causes depolarization. Describe what anatomical and physiological features these two classes of receptors have in common, and also the unique differences. Consider photoreceptors in mollusks, arthropod compound eyes, arthropod ocelli, annelids, and vertebrates.

2.8. Section 2.4.3 suggested that the Faraday streaming effect could induce an electric eld in and around a shark' s gill slits as seawater is forcefully expelled through them in the Earth's magnetic eld. The Earth's magnetic eld has, in general, a vertical and a horizontal component. (At the "magnetic equator," the vertical component is zero, and over the north and south magnetic poles, the horizontal component is zero.) As a rst approximation to modeling a hypothetical Faraday streaming effect magnetic sensor, consider the shark to be swimming at some low velocity that is small compared with the peak velocity of water expelled from the gill slits. Assume that water is expelled from the gill slits perpendicular to their (vertical) plane with peak velocity, vw. High peak water velocities can be obtained by muscular contraction of the pharynx.

In general, the Faraday streaming effect produces an electric eld gi ven by: E = vw • Be. The direction of E is normal to the plane containing vw and Be, and points in a direction a right-hand screw would advance when vw is rotated into Be. |e| = |ve| |Be| sin(.); is the angle between vw and Be. |e| is maximum when vw and Be are orthogonal.

Assume a model shark with one left and one right rectangular gill slit. Figure P2.8A shows a top view and a right side view of the right gill slit of a north-swimming shark. Note that for a shark pointing toward magnetic north anywhere in the oceans other than the magnetic equator or the magnetic poles, the dip angle, . , of Be will, in general, generate a Faraday E- eld in the plane of the gill aperture at an angle of (90° - .). The magnitude of this E eld will be vw Be because of orthogonality. Note that in the left gill aperture, the E eld will be 180° reversed from the right eld. That is, EL = -ER.

In Figure P2.8B, the model shark is swimming due east. Again, the right gill aperture is examined. (The geometry in this case is more complex.) Here it helps to break Be into its vertical and horizontal components. Because vwR is 180° from Bh, their cross-product is zero. The cross-product of vwR with Bv lies in the plane of the aperture and points anteriorly, producing a E eld with the orientation sho wn. (This approach is valid because the cross-product is distributive, i.e., A • (B + C) = A • B + A • C.)

a. Find the maximum E eld in micro volts/meter in the right gill aperture when vwR = 10 m/s, Bh = 17 ^T, and Bv = 55 ^T. Is this eld large

enough for ampullary electroreceptors located on the edges of the aperture to sense?

Find the magnitude and direction of E in the plane of the right aperture for a shark swimming northeast, and for a shark swimming southeast. Describe what happens to E in the right aperture when a shark swims south, west, northwest, and southwest. (Hint: De ne three orthogonal axes: x points north (direction of Bh), y points up, and z points east. i is a unit vector pointing in the +x direction, j is a unit vector pointing in the +y direction (up), and k is a unit vector pointing in the +z direction (east). The cross-product of two vectors described in rectangular coordinates can be written in general as

 i j k a a a x y z b b b x y z

Right gill aperture

(Right side view)