In this lab, you will need to be able to describe how multiple waves interact with each other. This does not add too much mathematical complexity to the wave equation (Eq. 2), and it allows us to develop a closer approximation of real-life situations as well (e.g. interacting ripple patterns in a pond, music, atomic physics, etc.). Here you will explore the superposition of two waves, y1 and y2, where y1 = sin(πx-2πt) and y2 = sin( πx2+2πt). Which of the following expressions accurately describes how these two distinct waves will combine? We call this interaction the principle of superposition.
1) y1 + y2 = sin(πx-2πt+ 2πx+2πt)=sin( 23πz)
2) y1 + y2 = sin(πx-2πt)+sin( 2πx+2πt)
3) y1 × y2 = sin((πx-2πt)×( 2πz+2πt))=sin( 22x2+xt-4t2)
4) y1 × y2 = sin(πx-2πt)×sin( 2πx+2πt)