What is the wavelength of a wave traveling through a rope if the distance from one crest to the next is 1m

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

Light from the sun reaches the earth in 8.3 minutes. the velocity is 3.00 x 10^8 m/s. how far is earth from the sun? i know how to get to d = (3 x 10^8 m/s)(498 sec). i just don't know how to get from there to the answer being 1.5 x 10^11 m.

Africtionless piston-cylinder contains 50 l of saturated liquid r-134a. the piston has a mass and an area resulting in an applied pressure of 500 kpa on the refrigerant. the refrigerant is now heated until its temperature rises to 70∘c. calculate the work (in kj) done during this process.