Dolphins emit clicks of sound for communication and echolocation. a marine biologist is monitoring a dolphin swimming in seawater where the speed of sound is 1520 m/s. when the dolphin is swimming directly away at 7.2 m/s, the marine biologist measures the number of clicks occuring per second to be at a frequency of 2210 hz. what is the difference (in hz) between this frequency and the number of clicks per second actually emitted by the dolphin?

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

Sobre transformações cíclicas, são feitas algumas afirmações, determine quais estão corretas. i – a variação de energia interna em uma transformação cíclica é nula; ii – o trabalho, em uma transformação cíclica, é sempre positivo; iii – ao completar um ciclo, o gás tem a mesma temperatura com a qual começou a transformação; iv – uma transformação cíclica é, obrigatoriamente, composta de transformações conhecidas, como adiabática, isocórica, etc: a) i e iii b) i e ii c) ii e iii d) i e iv e) iii e iv

Find the magnetic field a distance r from the center of a long wire that has radius a and carries a uniform current per unit area j in the positive z direction.