### Wave Motion and Displacement of a Rubber Ducky1. **Rubber Ducky Floating on Water Waves**: A rubber ducky (located at \( x = 0 \) m) floats on a lake and bobs up and down due to one-dimensional water waves. Shown to the right are two graphs: a \( y(t) \) graph depicting the vertical displacement of the rubber ducky as a function of time, and a \( y(x) \) graph depicting the water wave as a function of position at the time \( t = 0 \) s. #### Explanation of Graphs: **Graph 1: \( y(t) \) at \( x = 0 \)** - **Axes**: The vertical axis represents the displacement \( y \) in centimeters (cm), and the horizontal axis represents time \( t \) in seconds (s). - **Description**: This graph shows sinusoidal waves indicating the vertical movement of the rubber ducky over time. **Graph 2: \( y(x) \) at \( t = 0 \)** - **Axes**: The vertical axis represents the displacement \( y \) in centimeters (cm), and the horizontal axis represents position \( x \) in meters (m). - **Description**: This graph shows sinusoidal waves indicating the displacement of water at different positions along the x-axis at a fixed time (\( t = 0 \) s). #### Questions: a. **Determine the Wave Direction**: Explain how the \( y \) vs. \( t \) graph can tell whether the wave is moving to the right or to the left. b. **Equation of Motion**: Write out the equation of motion \( y(x,t) = A \sin \left( 2\pi \frac{x}{\lambda} \pm 2\pi \frac{t}{T} + \phi \right) + D \) for this wave and specify the values for \( A \), \( T \), \( \lambda \), \( \phi \), \( \pm \), and \( D \). #### Detailed Explanation of Graphs: **Graph 1: Displacement vs. Time (\( y(t) \))** - The oscillations indicate periodic vertical movements due to passing waves. - Peak-to-peak and trough-to-trough

SHM: simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion where…

1. A rubber ducky (located at x = 0 m) floats on a lake and bobs up and down due to one dimensional water waves. Shown to the right| are a y(t) graph that depicts the vertical displacement of rubber ducky as a function of time and a y(x) graph that depicts the water wave as a function of position at the time t= 0 s and. \y (in cm) at x=0 3 AAA t (in s) -1 -2 -3 \y (in cm) at t=0 a. Explain how the y vs. t graph tells you whether this wave is moving to the right or to the left. 3 2 1 x (in m) 1 2 3 -2 b. Write out the equation of motion y(x,t)= Asin 2n +2+)+D +D_for this wave. Make sure you T specify the values for A, T, , ø, ±, and D.

1. A rubber ducky (located at x = 0 m) floats on a lake and bobs up and down due to one dimensional water waves. Shown to the right| are a y(t) graph that depicts the vertical displacement of rubber ducky as a function of time and a y(x) graph that depicts the water wave as a function of position at the time t= 0 s and. \y (in cm) at x=0 3 AAA t (in s) -1 -2 -3 \y (in cm) at t=0 a. Explain how the y vs. t graph tells you whether this wave is moving to the right or to the left. 3 2 1 x (in m) 1 2 3 -2 b. Write out the equation of motion y(x,t)= Asin 2n +2+)+D +D_for this wave. Make sure you T specify the values for A, T, , ø, ±, and D.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

### Wave Motion and Displacement of a Rubber Ducky

1. **Rubber Ducky Floating on Water Waves**:
A rubber ducky (located at \( x = 0 \) m) floats on a lake and bobs up and down due to one-dimensional water waves. Shown to the right are two graphs: a \( y(t) \) graph depicting the vertical displacement of the rubber ducky as a function of time, and a \( y(x) \) graph depicting the water wave as a function of position at the time \( t = 0 \) s.

#### Explanation of Graphs:

**Graph 1: \( y(t) \) at \( x = 0 \)**
- **Axes**: The vertical axis represents the displacement \( y \) in centimeters (cm), and the horizontal axis represents time \( t \) in seconds (s).
- **Description**: This graph shows sinusoidal waves indicating the vertical movement of the rubber ducky over time.

**Graph 2: \( y(x) \) at \( t = 0 \)**
- **Axes**: The vertical axis represents the displacement \( y \) in centimeters (cm), and the horizontal axis represents position \( x \) in meters (m).
- **Description**: This graph shows sinusoidal waves indicating the displacement of water at different positions along the x-axis at a fixed time (\( t = 0 \) s).

#### Questions:
a. **Determine the Wave Direction**:
Explain how the \( y \) vs. \( t \) graph can tell whether the wave is moving to the right or to the left.

b. **Equation of Motion**:
Write out the equation of motion \( y(x,t) = A \sin \left( 2\pi \frac{x}{\lambda} \pm 2\pi \frac{t}{T} + \phi \right) + D \) for this wave and specify the values for \( A \), \( T \), \( \lambda \), \( \phi \), \( \pm \), and \( D \).

#### Detailed Explanation of Graphs:

**Graph 1: Displacement vs. Time (\( y(t) \))**
- The oscillations indicate periodic vertical movements due to passing waves.
- Peak-to-peak and trough-to-trough

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