The figure below shows a snapshot graph of a wave at t = Os moving to the left at 2 m/s. What is the history graph for this wave at x = 5 m, for t = -3 s to 2 s?

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### Wave Analysis: Understanding Its Motion Through Graphs

**Wave Snapshot:**

The primary graph presents a snapshot of a wave at \( t = 0 \) seconds, moving to the left at a speed of 2 m/s. The x-axis represents the position \( x \), while the y-axis represents the wave's amplitude \( y \). 

- The wave starts at zero amplitude at \( x = 0 \).
- From \( x = 0 \) to \( x = 2 \), the amplitude increases linearly to a maximum of 4.
- Between \( x = 2 \) and \( x = 4 \), the amplitude remains constant at 4.
- From \( x = 4 \) to \( x = 5 \), the amplitude decreases linearly back to zero.
- The wave then dips to an amplitude of -2 at \( x = 7 \) and increases to zero by \( x = 9 \).

**History Graphs:**

The four smaller sub-graphs (a, b, c, d) illustrate potential history graphs of the wave specifically at \( x = 5 \, \text{m} \), as it varies with time \( t \) from \(-3 \, \text{s} \) to \(2 \, \text{s} \).

- **Graph a):**
  - The amplitude starts at -2 at \( t = -3 \) and increases to 0.
  - Rising from 0 to 4, it remains constant before decreasing back to 0.

- **Graph b):**
  - Increases from 0 to 4, stays constant, and decreases symmetrically to -2, then returns to 0.

- **Graph c):**
  - Begins at a positive amplitude, drops to -2, then gradually rises to 4, and drops back to 0.

- **Graph d):**
  - Similar to others, showing approximately symmetric increases and decreases.

### Conclusion

Determining the correct history graph requires interpreting the initial wave's shape and its motion, calculating where the wave peak and troughs will appear as the wave moves leftward over the specified time frame.
Transcribed Image Text:### Wave Analysis: Understanding Its Motion Through Graphs **Wave Snapshot:** The primary graph presents a snapshot of a wave at \( t = 0 \) seconds, moving to the left at a speed of 2 m/s. The x-axis represents the position \( x \), while the y-axis represents the wave's amplitude \( y \). - The wave starts at zero amplitude at \( x = 0 \). - From \( x = 0 \) to \( x = 2 \), the amplitude increases linearly to a maximum of 4. - Between \( x = 2 \) and \( x = 4 \), the amplitude remains constant at 4. - From \( x = 4 \) to \( x = 5 \), the amplitude decreases linearly back to zero. - The wave then dips to an amplitude of -2 at \( x = 7 \) and increases to zero by \( x = 9 \). **History Graphs:** The four smaller sub-graphs (a, b, c, d) illustrate potential history graphs of the wave specifically at \( x = 5 \, \text{m} \), as it varies with time \( t \) from \(-3 \, \text{s} \) to \(2 \, \text{s} \). - **Graph a):** - The amplitude starts at -2 at \( t = -3 \) and increases to 0. - Rising from 0 to 4, it remains constant before decreasing back to 0. - **Graph b):** - Increases from 0 to 4, stays constant, and decreases symmetrically to -2, then returns to 0. - **Graph c):** - Begins at a positive amplitude, drops to -2, then gradually rises to 4, and drops back to 0. - **Graph d):** - Similar to others, showing approximately symmetric increases and decreases. ### Conclusion Determining the correct history graph requires interpreting the initial wave's shape and its motion, calculating where the wave peak and troughs will appear as the wave moves leftward over the specified time frame.
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