A traveling wave on a string can be described by the equation : y = (5.26 ~\text{m}) \cdot \sin \big( (1.65 ~\frac{\text{rad}}{\text{m}})x - (4.64 ~\frac{\text{rad}}{\text{sec}})t +(1.33 ~\text{rad}) \big)y=(5.26 m)⋅sin((1.65 m rad )x−(4.64 sec rad )t+(1.33 rad)) How much time will it take for a peak on this traveling wave to propagate a distance of 5.00 meters along the length of the string?

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.