Problem 36. Two transverse harmonic waves of the same frequency are combined. At the combination point the two waves have the forms y_{1}=A_{1} \cos \left(\omega t+\delta_{1}\right) u_{2}=A_{2} \cos \left(\omega t+\delta_{2}\right)

Find the amplitude of the total wave in the string if the total wave is written in the form y=y1+y2=A cos(wt+y)for the cases, \text { A) } A_{1}=1 \mathrm{~m}, A_{2}=1 \mathrm{~m}, \delta_{1}=0, \delta_{2}=\pi \text {. } \text { B) } A_{1}=1 \mathrm{~m}, A_{2}=1 \mathrm{~m}, \delta_{1}=0, \delta_{2}=0 \text {. } \text { C) } A_{1}=1 \mathrm{~m}, A_{2}=1 \mathrm{~m}, \delta_{1}=0, \delta_{2}=\pi / 2 \text {. } \text { D) } A_{1}=1 \mathrm{~m}, A_{2}=-2 \mathrm{~m}, \delta_{1}=0, \delta_{2}=\pi \text {. } \text { E) } A_{1}=1 \mathrm{~m}, A_{2}=2 \mathrm{~m}, \delta_{1}=0, \delta_{2}=\pi