Question

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.

Answer 1

- λ = 31.89

- f = 110.29Hz

- Ф = 2.39

Step-by-step explanation:

You have the following waveform expression:

`y(x,t)=ym\ sin(2.39+693t+0.197x)` (1)

The general expression for a wave can be written as:

`y(x,t)=y_o\ sin(kx\pm \omega t+\phi)` (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:

`\lambda=(2\pi)/(k)=(2\pi)/(0.197)=31.89m`

The wavelength of the wave is 31.89m

- The frequency is:

`f=(\omega)/(2\pi)=(693)/(2\pi)=110.29Hz`

The frequency of the wave is 110.29Hz

- The phase constant is 2.39