a. A matter wave $\Psi$ does not need a medium to travel, but a wave on a string does. The wavefunction $\Psi$ is a probability amplitude, and its square is proportional to the probability of finding the corresponding particle within a certain region of space. b. An EM wave does not require a medium to travel. The values of an EM wave are the electric and magnetic field vectors at that point, but a matter wave is a scalar. EM waves can be polarized, but matter waves cannot be.
Work Step by Step
a. The function describing a wave on a string gives the displacement of a piece of string from its equilibrium position.