identify the scenarios below as to whether they would increase, decrease, or not change the frequency in which a string vibrates and thus change its pitch. assume that no other changes are happening.
1. tightening a string for greater tension
2. replacing a thin string with a thick string
3. increasing the effective 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.

A26 cm object is 18 cm in front of a plane mirror. a ray of light strikes the object and is reflected off the mirror at a 42-degree angle. what is the angle of reflection? degrees what type of image is formed? what is the size of the image? cm

Which branches of natural science include the study of an organism that lived 10 million years ago