Why is 12 pi added at last ?

Q. Example 15.2 A wave travelling along a string is describe by,

      y (x ,t) = 0.005 sin (80.0 x – 3.0 t),

       in which the numerical constants are in SI units (0.005 m, 80.0 and m–1, and 3.0 rad S–1), Calculate (a) the amplitude. (b) the wavelength, and (c) the period and frequency of the wave. Also, calculate the displacement y of the wave at a distance x = 30.0 cm and time t = 20 s ?

   The displacement y at x = 30.0 cm and time t = 20 s is given by 

         y = (0.005 m ) sin ( 80.0 × 0.3 – 3.0 × 20)

             = (0.005 m) sin ( – 36 + 12  π )

            = (0.00 5 m) sin (1.699)

           = (0.005 m ) sin ( 970 5 mm
 

Dear Student,

 y = (0.005 m ) sin ( 80.0 × 0.3  3.0 × 20)y=0.005sin24-60y=0.005sin-36y=-0.005sin36this is in radian convert into degree36×180π=2062.65  degrewe know sin has the period of 360 degree.2062.65-5360=262.5y=-0.005sin262.5y=-0.005sin360-97.5y=0.005sin97.50.005 mmRegards
 

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