Bats produce calls for the echolocation of prey items; to do so, their calls need to bounce off the target and come back to them. sound waves tend to be reflected by objects larger or equal to the wavelength of the sound. for the following questions, use the appropriate values for cthat you find in your class notes.
(a) what minimum frequency (in khz) of calls would a bat need to produce to locate a 0.7inch moth?
(b) what is the period of a wave at this frequency?
(c) what would the wavelengthof this call be (in meters) if the bat were somehow to produce the sound in the water?
(d) what would the period of this waterbornewave be?

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.