Question

Consider the waveform expression. y(x,t)=ymsin(801t+3.38+0.503x) The transverse displacement ( y ) of a wave is given as a function of position ( x in meters) and time ( t in seconds) by the expression. Determine the wavelength, frequency, period, and phase constant of this waveform.

Answer 1

Answer:

f = 127.48 Hz ,  T = 7.844 1⁻³ s ,  Ф = 3.38 ,     λ = 12.49 m

Explanation:

The general equation for the motion of a wave in a string is

          y = A sin (kx -wt + fi)

the expression they give is

         y = ym sin (0.503x + 801 t + 3.38 )

the veloicda that accompanies time is

      w = 801   rad / s

angular velocity is related to frequency

      w = 2π f

      f = w / 2π

      f = 801 / 2π

      f = 127.48 Hz

The period is the inverse of the frequency

      T = 1 / f

       T = 1 / 127.48

      T = 7.844 10⁻³ s

the csntnate of phase fi is the independent term

      Ф = 3.38

the wave vector accompanies the position k = 0.503 cm

       ka = 2pi /λ

       λ = 2 π / k

       λ = 2 π / 0.503

       λ = 12.49 m