CALC Let is also a solution to the wave equation.

QUESTION:

Let \(y_{1}(x, t)=A \cos \left(k_{1} x-\omega_{1} t\right) \text { and } y_{2}(x, t)=A \cos \left(k_{2} x-\omega_{2} t\right)\) be two solutions to the wave equation, Eq. (15.12), for the same Show that \(y(x, t)=y_{1}(x, t)+y_{2}(x, t)\) is also a solution to the wave equation.

Equation Transcription:

Text Transcription:

y_1(x,t) = A cos (k_1x- \omega_1t) and y_2(x,t)=A cos (k_2x- \omega_2t)

y(x,t)=y_1(x,t)+y_2(x,t)