Bat Physics

Burrito Girl (my wife and sidekick) and I are vacationing in Estes Park, Colorado right now.  Last night we attended a Rocky Mountain National Park ranger talk entitled "Superheroes of the Night."  Bats, owls, mountain lions, and coyotes were dubbed "superheroes" for their unhuman physical adaptations.

The main purpose of the evening was to help the young NachoBoy earn his Junior Ranger badge.  He certainly enjoyed the talk, as one of his regular activities lately has been leanring to differentiate between the hoots of various owl species.

From a physics perspective, the owls piqued my interest.  Their ears are not aligned in the same vertical plane.  An owl's right ear is above the eye socket; the left ear is near chin level.  How does this help the owl survive?  An owl hunts from the branches of a tree, but is searching for prey on the ground.  The time delay of a sound hitting each ear can help the owl pinpoint the location of the animal.  People have pretty good directional sense about sound as well, but only in a horizontal plane around our head; the owl's ear position is well adapted to their sort of dive-bomb hunting.

Owls were fun, but bats... well, bats brought out the paper and pencil for a quick calculation.  And I'm still confused by this one, so help me out if you can.

Bats navigate and hunt principally using echolocation, i.e. sonar.  The park ranger last night described an experiment in which batologists* strung wire "less than the thickness of a piece of paper" around a darkened room.  A multitude of flying insects and bats were released in this room.  The wires were monitored to note each time that a bat collided with a wire.

*Or whatever they're called

What happened?  The bats ate all the insects, but never once touched a wire.  Conclusion:  Bats have pretty awesome sonar skills.

Here's where I brought out the paper-and-pen.  For the bat's sonar waves to reflect off of the paper-thin wires, the sonar wavelength has to be on the order of the wire thickness.  That's about 1/10 of a mm, or 10^-4 m.  The speed of sound is 340 m/s, or about 10² m.  Therefore, the frequency of the bat sonar has to be v/λ = 10⁶ Hz.  That's better known as 1 MHz, well above the ~50 kHz limit to human hearing.

I made a quick check on the reasonability of my calculation by asking the bat-savvy ranger if he had ever heard the bat's echolocation.  He said no -- he confirmed that the sound must be above the audible range, but he did not know the precise frequency.

A more involved internet search found this excellent discussion of the physics and biology of bat radar.  It states that the bat-recepticles are fine tuned to detect 60.0-61.5 kHz.  Bats use a wider range of outgoing frequencies, because then they will be able to detect the doppler-shifted return wave.  (Cool non-AP physics problem:  Calculate a reasonable range for outgoing bat frequencies for a reasonable range of insect speeds, such that the doppler-shifted return pulse will be in the 60.0 kHz range.)

But this fact contradicts my original calculation.  The wavelength of a bat's radar is (340 m/s)/(60,000 Hz) = 5 mm or so.  How, then, can the bat accurately detect something 50 times smaller, like a paper-width wire?

Clearly I'm not understanding something.  Can anyone out there explain?  If so, then I've got an excellent discussion for this year's waves unit.  Perhaps we can bring in a bat for demonstration purposes.

GCJ

(P.S. -- The picture at the top of the post is of a bat drinking.  Bats can't land to drink, because their gliding wings don't allow them to take off from the ground.  Airspeed velocity and such.  So they glide across standing water, lapping the water up with their tongues.  Awesome.)