Consider the waveform expression. < Feedback y (x, t) = ymsin (3.38 + 0.163x + 207t) One way to write the general expression for a traveling wave is The transverse displacement (y) of a wave is given as a function of position (x in meters) and time (t in seconds) by th expression. Determine the wavelength, frequency, period, and phase constant of this waveform. y = ymsin (kx ± ot + 4o) The order of the terms is unimportant, but the wavenumber (k) is always the meters f = coefficient of the position (x) and the 45.548 ×105 65.8636 angular frequency (@) is always the Incorrect coefficient of the time (t). Incorrect How are k and o related to the T = seconds Po = wavelength, frequency, and period? 0.01518 3.38 What is the phase constant? Incorrect

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Chapter1: Units, Trigonometry. And Vectors
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I was given wrong answer, pls help

**Consider the waveform expression**

\[ y(x,t) = y_m \sin (3.38 + 0.163x + 207t) \]

The transverse displacement (\(y\)) of a wave is given as a function of position (\(x\) in meters) and time (\(t\) in seconds) by the above expression.

### Task
Determine the wavelength (\(\lambda\)), frequency (\(f\)), period (\(T\)), and phase constant (\(\phi_0\)) of this waveform.

### Provided Answers and Feedback
The student has provided the following answers, but they are marked as incorrect.

- **Wavelength (\(\lambda\))**: 
  \[
  45.548 \times 10^5 \text{ meters}
  \]

- **Frequency (\(f\))**: 
  \[
  65.8636 \text{ Hz}
  \]

- **Period (\(T\))**:
  \[
  0.01518 \text{ seconds}
  \]

- **Phase constant (\(\phi_0\))**:
  \[
  3.38
  \]

These answers are marked incorrect.

### Explanation from Feedback
**One way to write the general expression for a traveling wave is**:
\[ y = y_m \sin (kx \pm \omega t + \phi_0) \]

The order of the terms is unimportant, but:
- The wavenumber (\(k\)) is always the coefficient of the position (\(x\)).
- The angular frequency (\(\omega\)) is always the coefficient of the time (\(t\)).

**How are \(k\) and \(\omega\) related to the wavelength, frequency, and period?**
- **Wavenumber (\(k\))**:
  \[
  k = \frac{2\pi}{\lambda}
  \]

- **Angular frequency (\(\omega\))**:
  \[
  \omega = 2\pi f
  \]

### Clarifying the Values from the Waveform Equation:
Given the waveform \(y(x,t) = y_m \sin (3.38 + 0.163x + 207t)\):

- **Wavenumber (\(k\))**:
  \[
  k = 0.163 \text{ m}^{-1
Transcribed Image Text:**Consider the waveform expression** \[ y(x,t) = y_m \sin (3.38 + 0.163x + 207t) \] The transverse displacement (\(y\)) of a wave is given as a function of position (\(x\) in meters) and time (\(t\) in seconds) by the above expression. ### Task Determine the wavelength (\(\lambda\)), frequency (\(f\)), period (\(T\)), and phase constant (\(\phi_0\)) of this waveform. ### Provided Answers and Feedback The student has provided the following answers, but they are marked as incorrect. - **Wavelength (\(\lambda\))**: \[ 45.548 \times 10^5 \text{ meters} \] - **Frequency (\(f\))**: \[ 65.8636 \text{ Hz} \] - **Period (\(T\))**: \[ 0.01518 \text{ seconds} \] - **Phase constant (\(\phi_0\))**: \[ 3.38 \] These answers are marked incorrect. ### Explanation from Feedback **One way to write the general expression for a traveling wave is**: \[ y = y_m \sin (kx \pm \omega t + \phi_0) \] The order of the terms is unimportant, but: - The wavenumber (\(k\)) is always the coefficient of the position (\(x\)). - The angular frequency (\(\omega\)) is always the coefficient of the time (\(t\)). **How are \(k\) and \(\omega\) related to the wavelength, frequency, and period?** - **Wavenumber (\(k\))**: \[ k = \frac{2\pi}{\lambda} \] - **Angular frequency (\(\omega\))**: \[ \omega = 2\pi f \] ### Clarifying the Values from the Waveform Equation: Given the waveform \(y(x,t) = y_m \sin (3.38 + 0.163x + 207t)\): - **Wavenumber (\(k\))**: \[ k = 0.163 \text{ m}^{-1
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