Which of the following scenarios describes a condition in which resonance can occur?

a. two tuning forks that vibrate at the same frequency are near each other. one tuning fork is struck with a mallet so that it vibrates.
b. two tuning forks are struck simultaneously, one with a frequency of 659hz and one with a frequency of 639 hz, causing beats.
c. a tuning fork is over a column of air that is 9/2 the wavelength of the wave produced by the tuning fork.
d. an isolated tuning fork is struck with a mallet, causing it to vibrate strongly at 659 hz.

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele