Question

Given two wave equations, ?1 (?,?) = ? sin(?? − ?? + ?1 ) and ?2 (?,?) = ? sin(?? − ?? + ?2 ), what is the linear combination of the two wave equations where both waves have the same wavelength and angular frequency but ? ≠ ? and ?1 ≠ ?2? That is, what is ?1 + ?2 given different amplitudes of oscillation and phase constants? Your answer must be in the form of ?3 (?,?) = ? sin(?? − ?? + ?3 ) where ? is the amplitude of oscillation of the new resultant wave and ?3 is a new phase constant. Be sure to give an expression for ? and ?3. Show how you get to your answer. Do not simply show an end result. Hint: Trigonometric identities will be useful here.

Answer 1