## Alternative Homework Assignment: Echolocation

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# Alternative Homework Assignment: Echolocation

The ability to see in the dark is a great advantage for a predator to have over its prey or its competition. For this reason, many animals have developed this adaptation in one form or another. Cats, for example, have eyes that are extremely sensitive to small amounts of light. This allows them to see in near darkness. However, some animals are able to detect objects at a distance in complete darkness. These animals use high frequency sound to form images via a system called echolocation. Two of the more famous users of this type of sensation are bats and dolphins. In this problem, we will try to estimate how clearly these animals can "see" with sound.

 Part 1: a) Eptesicus Fuscus or the North American Big Brown Bat uses clicks that vary in sound frequency from 20 kHz to 100 kHz. On a warm summer night, what wavelength range does this correspond to? b) One way to measure how "clearly" something can be seen is to measure how far apart two objects have to be before they are distinguishable as two objects. This of course depends on how far away the objects are. If the bats are able to use their two ears as an interferometer, then the bat is able to distinguish two objects if the angle between the objects that has the bat as its vertex is greater than the angular separation of the central maximum and the first minimum of the interference pattern from one of the objects. If the bat's ears are 1 cm apart, what is the resolution for the smallest wavelength of sound used?

c) Bats have experimentally been shown to be able to resolve objects with a resolution angle of 8 degrees. Is it possible that bats use their ears as an interferometer? How else might the bats achieve this resolution?

d) Estimate the range at which a bat can pick out individual mosquitoes from a swarm. Estimate the range at which the bat can resolve a mosquito's wings.

 Part 2: a) Dolphins use frequencies up to 140 kHz in their echolocation. Remembering that dolphins use this in water, what is the associated wavelength? b) Does being in water help or harm the dolphins' ability to "see" with sound? c) With an ear separation of about 45 cm, what is the dolphin's resolution angle if they use their ears as an interferometer?

Part 3:

a) To get an idea of how clear the dolphin and bat sense images are, consider the resolution of human vision. Humans do not use their eyes as an interferometer, so the relevant equation is for a circular aperture diffraction pattern. Since light has a wavelength of about 600 nm and the radius of the pupil is about 5mm, what is the human angle of resolution?

b) Why do bats and dolphins still have eyes?

These problems written and collected by K. Vick, E. Redish, and P. Cooney. These problems may be freely used in classrooms. They may be copied and cited in published work if the Activity-Based Physics (ABP) Alternative Homework Assignments (AHAs) Problem site is mentioned and the URL given.

 Work supported in part by NSF grant DUE-9455561

To contribute problems to this site, send them to redish@quark.umd.edu.

Maintained by University of Maryland PERG
Comments and questions may be directed to E. F. Redish