A student must determine how the mass per unit length of a string affects the wavelength of standing waves produced on a string that is fixed at both ends. One end of a string is attached to an oscillator, and the other end passes over a pulley and is connected to a hanging block of weight 10 N. The frequency of the oscillator is kept constant at 400 . Three strings made from the same material but of different masses are used in the experiment. The length L of each string is varied to create the first possible standing wave, as shown in the figure. The table shows the length, mass per unit length, and frequency of oscillation for each string that was tested. Does the mass per unit length of a string affect the wavelength of the first possible standing wave?

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.

Asmall object with mass 0.200 kg swings back and forth on the lower end of a light rope that is 3.00 m long. the upper end of the rope is attached to the ceiling. as the object swings through its lowest position, where the rope is vertical, the speed of the object is 5.80 m/s. at this point in the motion, what is the tension in the rope? (use g = 9.80 m/s2.)

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