### Standing Waves in a Pipe with Air ColumnConsider 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.

Part (a) : The correct image is 2nd image. Part (b): Wavelength is 2.33 m.

Consider standing waves in a pipe of length L = 3.5 m containing a column of air. The speed of sound in the columns is v. = 334 m/s. Each of the standing wave images provided may represent a case for which one or both ends are open. ▷ A 20% Part (a) Select the image from the options provided showing the gas pressure for the third harmonic of a pipe with two open ends. Grade Summary Deductions Potential 0% 100% Submissions о Attempts remaining: 100 (0% per attempt) detailed view O O Submit Hint Feedback I give up! Hints: 0 for a 0% deduction. Hints remaining: 0 Feedback: A 20% Part (b) Calculate the wavelength 3 in m for the third harmonic in the pipe with two open ends. Ө

Consider standing waves in a pipe of length L = 3.5 m containing a column of air. The speed of sound in the columns is v. = 334 m/s. Each of the standing wave images provided may represent a case for which one or both ends are open. ▷ A 20% Part (a) Select the image from the options provided showing the gas pressure for the third harmonic of a pipe with two open ends. Grade Summary Deductions Potential 0% 100% Submissions о Attempts remaining: 100 (0% per attempt) detailed view O O Submit Hint Feedback I give up! Hints: 0 for a 0% deduction. Hints remaining: 0 Feedback: A 20% Part (b) Calculate the wavelength 3 in m for the third harmonic in the pipe with two open ends. Ө

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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Concept explainers

Interference of sound

Seiche

A seiche is an oscillating standing wave in a body of water. The term seiche pronounced saysh) can be understood by the sloshing of water back and forth in a swimming pool. The same phenomenon happens on a much larger scale in vast bodies of water including bays and lakes. A seizure can happen in any enclosed or semi-enclosed body of water.

Question

### 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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