1. Consider two waves that are superposing. Both waves are traveling along the z axis. Wave 1 is polarized horizontally, and wave 2 is polarized vertically. At a particular moment, the displacement of each wave is given by:

d₁(z) = 5.1 cos(5 z), and

d₂(z) = 3.6 cos(4 z).

Calculate the total displacement of the medium at z = 1.9 m, in m. Your calculator should be in radians mode for this question.

2. It is known that longitudinal waves travel at 9,225 m/s, and transverse waves travel at 3,062 m/s through the Earth's crust. An earthquake occurs. The transverse waves generated by the quake arrive 8 s after the longitudinal waves. How far away was the earthquake, in m?

3. Consider a longitudinal wave traveling along the x axis. At a particular instant, the displacement of the wave as a function of position is given by:

d(x) = 3.1 sin( 2.4 x ) (m)

Here positive values of d represent forward displacements in the +x direction. Before the wave traveled through the medium, the distance between location x = 5.7 m and x = 19.6 m was just (19.6 - 5.7) m. Calculate the distance between these points when the wave is passing through it, in m. Your calculator should be in radians mode for this question.