1) Determine A for the following wave and report it.

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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**Instructions for Wave Measurements:**

**Introduction:**

The following questions ask you to calculate various things about the waves represented in the figures. While there is some play in the answers to accommodate differing opinions on measurement, the range of acceptable answers is not so large as to allow sloppiness in the reading of the plots’ information. The required precision of the answers is tied to the scale available - exactly the same skill developed in the lab activity that asked you to practice reading a balance.

You don’t need to print this out to take measurements. If you’re viewing this on a computer, you can drag the corner of another window over the images to serve as a straightedge to take a better measurement than just “eyeballing it.” The plots have top and right axes hashings to help make sure your straightedge is level when measuring, and I've made the plots rather large. If you only have a phone available to access this information (so using a separate browser window edge as a straightedge is not an option), most phones will let you take a screenshot that you can crop to take a measurement, then discard. Let me know if you need help figuring something like that out.

Help yourself out, whenever possible, by spreading out measurement error over a larger range. For instance, measure the length of all wavelengths available or at least as many as are easy to identify in quarter- or half-wavelength increments and divide that length by how many wavelengths there are instead of trying to measure a single wavelength directly. If you have the same measurement error for a measurement of length that represents three wavelengths vs a length that represents only one wavelength, that error impacts the former much less than the latter. The answers to these problems are coded assuming you have made the measurement to the best precision available.

**Measurement Instructions:**

1. **Measure / Calculate the most precise possible answer** you can and report the answer in the field.
2. **Report more digits than are significant** and do not include the unit - the system is expecting the standard unit, so if necessary convert your answer into the appropriate unit before reporting.

**Question:**

**1) Determine λ for the following wave and report it.**

**Note:** Use the provided graphs and measurement principles to determine the wavelength (λ) and ensure accuracy by averaging over multiple wavelengths if possible.
Transcribed Image Text:**Instructions for Wave Measurements:** **Introduction:** The following questions ask you to calculate various things about the waves represented in the figures. While there is some play in the answers to accommodate differing opinions on measurement, the range of acceptable answers is not so large as to allow sloppiness in the reading of the plots’ information. The required precision of the answers is tied to the scale available - exactly the same skill developed in the lab activity that asked you to practice reading a balance. You don’t need to print this out to take measurements. If you’re viewing this on a computer, you can drag the corner of another window over the images to serve as a straightedge to take a better measurement than just “eyeballing it.” The plots have top and right axes hashings to help make sure your straightedge is level when measuring, and I've made the plots rather large. If you only have a phone available to access this information (so using a separate browser window edge as a straightedge is not an option), most phones will let you take a screenshot that you can crop to take a measurement, then discard. Let me know if you need help figuring something like that out. Help yourself out, whenever possible, by spreading out measurement error over a larger range. For instance, measure the length of all wavelengths available or at least as many as are easy to identify in quarter- or half-wavelength increments and divide that length by how many wavelengths there are instead of trying to measure a single wavelength directly. If you have the same measurement error for a measurement of length that represents three wavelengths vs a length that represents only one wavelength, that error impacts the former much less than the latter. The answers to these problems are coded assuming you have made the measurement to the best precision available. **Measurement Instructions:** 1. **Measure / Calculate the most precise possible answer** you can and report the answer in the field. 2. **Report more digits than are significant** and do not include the unit - the system is expecting the standard unit, so if necessary convert your answer into the appropriate unit before reporting. **Question:** **1) Determine λ for the following wave and report it.** **Note:** Use the provided graphs and measurement principles to determine the wavelength (λ) and ensure accuracy by averaging over multiple wavelengths if possible.
### Position Space Representation of a Wave

#### Description of the Graph:
The graph provided illustrates a wave traveling through space. The horizontal axis represents the **distance of travel (x)** in meters [m], spanning from 0 to 5 meters. The vertical axis represents the **distance y, [also in meters (m)]**, ranging from -5 to 5 meters.

The wave depicted is a sinusoidal wave, characterized by its periodic oscillations:

- **Amplitude**: The amplitude of the wave is 5 meters, as it oscillates from -5 to 5 meters.
- **Period (T)**: This is the horizontal distance required for the wave to complete one full cycle.

#### Instructions:
2) **Determine T for the following wave and report it.**

To determine the period \( T \) of the wave, identify the distance between two corresponding points in consecutive cycles on the horizontal axis. This could be, for instance, the distance from one peak to the next or from one trough to the next.

**Calculation Steps:**
1. Observe a peak at approximately \( x = 0 \) meters.
2. The next peak appears at approximately \( x = 1 \) meters.
3. Therefore, the period \( T \) is approximately 1 meter.

Reporting the period \( T \):

\[ \text{Period } (T) = 1 \text{ meter} \]

This represents the distance each wave travels to complete a full cycle.

### Summary
- **Graph Title**: Position Space Representation
- **X-axis**: Distance of travel \( x \) [m]
- **Y-axis**: Distance \( y \) [m]
- **Wave Characteristics**: Sinusoidal wave
- **Amplitude**: 5 meters
- **Period (T)**: \(\approx 1 \text{ meter} \)
Transcribed Image Text:### Position Space Representation of a Wave #### Description of the Graph: The graph provided illustrates a wave traveling through space. The horizontal axis represents the **distance of travel (x)** in meters [m], spanning from 0 to 5 meters. The vertical axis represents the **distance y, [also in meters (m)]**, ranging from -5 to 5 meters. The wave depicted is a sinusoidal wave, characterized by its periodic oscillations: - **Amplitude**: The amplitude of the wave is 5 meters, as it oscillates from -5 to 5 meters. - **Period (T)**: This is the horizontal distance required for the wave to complete one full cycle. #### Instructions: 2) **Determine T for the following wave and report it.** To determine the period \( T \) of the wave, identify the distance between two corresponding points in consecutive cycles on the horizontal axis. This could be, for instance, the distance from one peak to the next or from one trough to the next. **Calculation Steps:** 1. Observe a peak at approximately \( x = 0 \) meters. 2. The next peak appears at approximately \( x = 1 \) meters. 3. Therefore, the period \( T \) is approximately 1 meter. Reporting the period \( T \): \[ \text{Period } (T) = 1 \text{ meter} \] This represents the distance each wave travels to complete a full cycle. ### Summary - **Graph Title**: Position Space Representation - **X-axis**: Distance of travel \( x \) [m] - **Y-axis**: Distance \( y \) [m] - **Wave Characteristics**: Sinusoidal wave - **Amplitude**: 5 meters - **Period (T)**: \(\approx 1 \text{ meter} \)
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