In a pipe closed at one end and filled with air, a 384-Hz tuning fork resonates when the pipe is 22 cm long; this tuning fork does not resonate for any smaller pipes. a. State three other lengths at which this pipe will resonate with the 384-Hz tuning fork. b. The end of the pipe that was closed is now opened, so that the pope is open at both ends. Describe any changes in the lengths of pipe that will resonate with the 384-Hz tuning fork. c. The air in the closed pipe is replaced with helium. Describe an experiment that would use the pipe to determine the speed of sound in helium.

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.