transverse wave on a string is described by wave function:y=(0.120m)sin((/8)x+4t

Question

transverse wave on a string is described by wave function:y=(0.120m)sin((/8)x+4t) The problem asks to find the transverse speed and accelerationof an element of the string at t=.200s forthe point on string located at x=1.6m. would the transversed speed be the derivative of y in regardsto t. v=(4)(0.120m)cos((/8)+4t) Thusplugging in values of t and x given is the correct answer fortransverse speed (1.5m/s) If this is not the correct answer pleasegive me a hint as to what I did wrong. transverse wave on a string is described by wave function:y=(0.120m)sin((/8)x+4t) The problem asks to find the transverse speed and accelerationof an element of the string at t=.200s forthe point on string located at x=1.6m. would the transversed speed be the derivative of y in regardsto t. v=(4)(0.120m)cos((/8)+4t) Thusplugging in values of t and x given is the correct answer fortransverse speed (1.5m/s) If this is not the correct answer pleasegive me a hint as to what I did wrong.

Explanation / Answer

      y=(0.120m)sin((/8)x+4t) transverse speed, v = dy / dt =  (4) (0.120)cos [ (/8)x + 4t ]                             = (4) (0.120) cos [ (/8) (1.6 )+ 4 (0.2) ]                              = 1.5 cos ( 0.2 + 0.8 )                               =1.5 cos                               =- 1.5 m/s acceleration, a = dv / dt =   - (4) (4) (0.120) sin [ (/8)x + 4t ]                                     = - 16 2 (0.12) sin [ (/8) (1.6 )+ 4(0.2) ]                                     =  - 16 2 (0.12) sin ( 0.2 + 0.8)                                     =  -16 2 (0.12) sin                                       =0

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