Question

In general, the cosine function has maximum displacements, either positive or negative, when its argument is equal to an integer multiple of π. When t = 0.150 s , k = 12.8 rad/m , and ω = 109 rad/s use the wave equation to select all of the x positions that correspond to points of maximum displacement.

check all that appy

0.760 m

1.52 m

1.65 m

1.77 m

1.89 m

2.01 m

Answer 1

The equation of wave traveling in positive x is as follows: Y(x,t) = A cos(kx -wt) Here, the displacement is Y , the amplitude is A, the wave number is k , the distance along x direction isx , the angular frequency is o and the time ist. The displacement is, A cos(kx - wt)= +1 kx-wt =nt ni + wt x= Substituting each value of displacements, For n=1 (12.8rad/m) =1.52 m For n=2 (2)(T)+(109rad/s)(0.150 s) (12.8rad/m) = 1.77 m

For n=3 (3)(A)+(109 rad/s)(0.150 s) (12.8 rad/m) = 2.01m The values of x correspond to maximum displacement are, 1.52 m 1.77m 2.01m