Which of the following wave functions satisfies the wave equation,\frac{\partial^{2} y(x, t)}{\partial x^{2}}=\frac{1}{v^{2}} \frac{\partial^{2} y(x, t)}{\partial t^{2}}∂x 2∂ 2y(x,t)= v 2 1∂t 2∂ 2 y(x,t)? (a) y(x, t)=A \cos (k x+\omega t)y(x,t)=Acos(kx+ωt); (b) y(x, t)=A \sin (k x+\omega t)y(x,t)=Asin(kx+ωt); (c) y(x, t)=A (\cos k x +\cos \omega t)y(x,t)=A(coskx+cosωt) (d) For the wave of part (b), write the equations for the transverse velocity and transverse acceleration of a particle at point x.