The first five harmonics for a vibrating string are shown in figure 24.13. a. for each harmonic, identify the number of wavelengths represented. b. for each harmonic, identify the number of nodes and antinodes that are present (include the ends of the string in your count). c. which of the five harmonics has the highest natural frequency? d. make a drawing that shows what the sixth harmonic would look like.

Large electric fields in cell membranes cause ions to move through the cell wall. the field strength in a typical membrane is 1.0 x 10 7 n/c. what is the magnitude of the force on a calcium ion with charge +e? what is its acceleration? is it possible for a particle with the same charge as as calcium to have a different acceleration if placed at this location? what would change the acceleration: mass of the particle? diameter of the particle?