Question

If y(x, t) = (5.4 mm)sin(kx + (575 rad/s)t + ϕ) describes a wave traveling along a string, how much time does any given point on the string take to move between displacements y = +2.0 mm and y = −2.0 mm?

If y(x, t) = (5.4 mm)sin(kx + (575 rad/s)t + φ) describes a wave traveling along a string, how much time does any given point on the string take to move between displacements y = +2.0 mm and y =-2.0 mm? 0.00132s

Answer 1

Given

wave equation is y(x, t) = (5.4 mm)sin(kx + (575 rad/s)t + ϕ)

time taken by the point move between displacements y = +2.0 mm and y = −2.0 mm? is  

v = y/t ==> t = y/v

v(t) = dy(t)/dt= 5.4*575cos(575) = -2543.4671 mm/s

t = (2-(2))/2543.4671 s

t = 0.0015727 s

so time taken is t = 0.0015727 s