Consider the waveform expression. y(x,t)=ymsin(2.39+693t+0.197x) 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.

Respuesta :

Answer:

-   λ = 31.89

-   f = 110.29Hz

-   Ф = 2.39

Explanation:

You have the following waveform expression:

[tex]y(x,t)=ym\ sin(2.39+693t+0.197x)[/tex]      (1)

The general expression for a wave can be written as:

[tex]y(x,t)=y_o\ sin(kx\pm \omega t+\phi)[/tex]          (2)

The sign of the term wt determines the direction of the motion of the wave.

In comparison with the equation (1) you have:

k: wavenumber = 0.197

w: angular frequency = 693

Ф: phase constant of the wave = 2.39

- The wavelength of the wave is given by the following formula:

[tex]\lambda=\frac{2\pi}{k}=\frac{2\pi}{0.197}=31.89m[/tex]

The wavelength of the wave is 31.89m

- The frequency is:

[tex]f=\frac{\omega}{2\pi}=\frac{693}{2\pi}=110.29Hz[/tex]

The frequency of the wave is 110.29Hz

- The phase constant is 2.39