College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![### Standing Waves in a Pipe with Air Column
Consider standing waves in a pipe of length \( L = 3.5 \, \text{m} \) containing a column of air. The speed of sound in the columns is \( v_s = 334 \, \text{m/s} \). Each of the standing wave images below may represent a scenario in which one or both ends of the pipe are open.
#### 20% Part (a)
**Question:**
Select the image from the options provided showing the gas pressure for the third harmonic of a pipe with two open ends.
**Options:**
(Images are provided showing various pressure distributions in a pipe, with differing densities of dots to indicate pressure levels).
- Select the correct image by clicking the corresponding radio button.
- **Grade Summary:**
- Deductions: 0%
- Potential: 100%
- Submissions: Attempts remaining: 100 (0% per attempt)
**Explanation of Diagrams:**
The correct image will show a standing wave pattern characteristic of the third harmonic in a pipe open at both ends. Typically, for an open-open pipe, each end is an antinode, and the third harmonic would have three nodes and four antinodes.
![Diagram Legend]
- Higher concentration of dots: Higher gas pressure
- Lower concentration of dots: Lower gas pressure
(Select the image that correctly represents these criteria.)
#### 20% Part (b)
**Question:**
Calculate the wavelength \( \lambda_3 \) in meters for the third harmonic in the pipe with two open ends.
**Hints:**
There are 0 hints remaining for a 0% deduction.
**Feedback:**
[Field to display feedback after submission]
---
#### Solution to Part (b):
1. The formula for the wavelength of the nth harmonic in an open pipe is:
\[ \lambda_n = \frac{2L}{n} \]
2. For the third harmonic (\( n = 3 \)):
\[ \lambda_3 = \frac{2 \times 3.5 \, \text{m}}{3} = \frac{7 \, \text{m}}{3} \approx 2.33 \, \text{m} \]
Submit your answers and review the feedback provided.](https://content.bartleby.com/qna-images/question/b452b854-6604-410e-8d22-3631c869b23c/d6732478-1a9f-4810-aad8-7edd23b1e83e/cyxobse_processed.png)
Transcribed Image Text:### Standing Waves in a Pipe with Air Column
Consider standing waves in a pipe of length \( L = 3.5 \, \text{m} \) containing a column of air. The speed of sound in the columns is \( v_s = 334 \, \text{m/s} \). Each of the standing wave images below may represent a scenario in which one or both ends of the pipe are open.
#### 20% Part (a)
**Question:**
Select the image from the options provided showing the gas pressure for the third harmonic of a pipe with two open ends.
**Options:**
(Images are provided showing various pressure distributions in a pipe, with differing densities of dots to indicate pressure levels).
- Select the correct image by clicking the corresponding radio button.
- **Grade Summary:**
- Deductions: 0%
- Potential: 100%
- Submissions: Attempts remaining: 100 (0% per attempt)
**Explanation of Diagrams:**
The correct image will show a standing wave pattern characteristic of the third harmonic in a pipe open at both ends. Typically, for an open-open pipe, each end is an antinode, and the third harmonic would have three nodes and four antinodes.
![Diagram Legend]
- Higher concentration of dots: Higher gas pressure
- Lower concentration of dots: Lower gas pressure
(Select the image that correctly represents these criteria.)
#### 20% Part (b)
**Question:**
Calculate the wavelength \( \lambda_3 \) in meters for the third harmonic in the pipe with two open ends.
**Hints:**
There are 0 hints remaining for a 0% deduction.
**Feedback:**
[Field to display feedback after submission]
---
#### Solution to Part (b):
1. The formula for the wavelength of the nth harmonic in an open pipe is:
\[ \lambda_n = \frac{2L}{n} \]
2. For the third harmonic (\( n = 3 \)):
\[ \lambda_3 = \frac{2 \times 3.5 \, \text{m}}{3} = \frac{7 \, \text{m}}{3} \approx 2.33 \, \text{m} \]
Submit your answers and review the feedback provided.
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