The superposition of these waves is given by: \[\begin{aligned} D(x,t) &= D_1(x,t) + D_2(x,t)\\ &=A\Bigr(\sin(kx-\omega t)+\sin(kx+\omega t)\Bigl)\end{aligned}\] We can use the following trigonometric...The superposition of these waves is given by: \[\begin{aligned} D(x,t) &= D_1(x,t) + D_2(x,t)\\ &=A\Bigr(\sin(kx-\omega t)+\sin(kx+\omega t)\Bigl)\end{aligned}\] We can use the following trigonometric identity to combine these into a single term: \[\begin{aligned} \sin\theta_1+\sin\theta_2 = 2\sin\left(\frac{\theta_1+\theta_2}{2} \right) \cos\left( \frac{\theta_1-\theta_2}{2}\right)\end{aligned}\] The resulting wave is thus given by: \[\begin{aligned} D(x,t) &= 2A\sin\left(\frac{kx-\omega t + k…
