problem 36 two transverse harmonic waves of the same frequency are com

Question

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