Question

CONSIDER THE WAVE FUNCTION Y X , T = 0.015COS 8X-80T CALCULATE THE PARTICLE VELOCITY AND PARTICLE ACCELERATION AT Y 0.01 , 0.4)

Answer 1

$y(x,t)=0.015\cos(8x-80t),$

$y_0=(0.01,0.4).$

$v_p(x,t)=\frac{\partial y}{\partial x}=\\-8\cdot 0.015\sin(8x-80t),$

$v_p(y_0)=0.058~\frac ms,$

$a_p=\frac{\partial v_p}{\partial x}=\\-64\cdot 0.015\cos(8x-80t),$

$a_p(y_0)=-0.841~\frac m{s^2}.$