Question

高一下数学题（与三角函数有关）平静的湖面上,一棵松子悄然落下,激起层层涟漪,假设水波起伏的高度y（cm）（记平静时的水面

Answer 1

1.第一颗松子落下的波形:y1=－2sintπ/6

第二颗松子落下的波形:y2=－2sin(t-2)π/6,

所以两列波叠加得:y=－2sintπ/6－2sin(t-2)π/6

=-2*2sin[(tπ/6)+(t-2)π/6]cos[tπ/6)-(t-2)π/6]

=-4sin[(t-1)π/3]cos(π/3)

=-2sin[(t-1)π/3]

2.即求t=9(s)时,y=-2sin[(9-1)π/3]=-2sin（2π/3）= 负的根号3