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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.

1 Answer

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Answer:

- 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

User Paul Peelen
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