Consider two sinusoidal sine waves traveling along a string, modeled as y1(x, t) = 0.3 msin(4 m−1 x+3 s−1 t+π3) and y2(x, t) = 0.6 msin(8 m−1 x−6 s−1 t). What is the height of the resultant wave formed by the interference of the two waves at the position x = 1.0 m at time t = 3.0 s?
![Two traveling waves, y1(x, t) and y2(x, t), are generated on the same taut string. Individually, the two traveling waves can be described by the two equations y1(x, t) = (1.73 cm)sin[k1 x+(0.173 rad/s)t+ϕ1]y2(x, t) = (6.03 cm)sin[k2 x−(7.76 rad/s)t+ϕ2] where k1 and k2 are the wave numbers and ϕ1 and ϕ2 are the phase angles. If both of the traveling waves exist on the string at the same time, what is the maximum positive displacement Δy that a point on the string can ever have? Δy = cm What are the smallest positive values of the unknown phase constants ϕ1 and ϕ2 (in radians) such that the maximum displacement occurs at the origin (x = 0) at time t = 2.01 s? ϕ1 = rad ϕ2 = rad](https://www.doubtrix.com/uploads/editor/8679972707YOXKefHWXJ.png)
