Two identical forward-facing loudspeakers are 35.2 cm apart. They are both connected to a signal generator that makes them vibrate in phase at a frequency of 1.98 kHz. (Take the speed of sound as 340 m/s. Consider nonnegative angles only. Enter your answers from smallest to largest, starting with the smallest answer in the first answer blank below. (a) At what angles (in degrees), measured from the perpendicular bisector of the line joining the speakers, would a distant observer hear maximum sound intensity?
(b) At what angles (in degrees) would such an observer hear minimum sound intensity?

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.