Two waves traveling on a string in the same direction both have a frequency of 92 Hz, a wavelength of 0.19 m, and an amplitude of 0.32 m. What is the amplitude of the resultant wave if the original waves differ in phase by pi /3 rad?

Question

Two waves traveling on a string in the same direction both have a frequency of 92 Hz, a wavelength of 0.19 m, and an amplitude of 0.32 m. What is the amplitude of the resultant wave if the original waves differ in phase by pi /3 rad? 
What is the phase difference between the two waves if the amplitude of the resultant wave is 0.25 m?

bobpursley · Answer

consider your trig

A1 *cos(wt+theta1) + A2 cos(wt+theta2)
= A3 * cos(wt+Theta3)
where
A3^2=(A1cosTheta1 +A2cosTheta2)^2+(A1sinTheta1+A2sinTheta2)^2

and Theta3 is given by

arc tan ( (A1SinTheta1+A2SinTheta2)/(A1cosTheta1+A2CosTheta1) )