A standing wave is created in the organ pipe as shown. The frequency of the sound from this standing wave is 300 Hz. What is the fundamental frequency of the organ pipe? (Hint: work in variables first and then plug numbers in only at the very end) XXX
A standing wave is created in the organ pipe as shown. The frequency of the sound from this standing wave is 300 Hz. What is the fundamental frequency of the organ pipe? (Hint: work in variables first and then plug numbers in only at the very end) XXX
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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![**Understanding Standing Waves in Organ Pipes**
In this example, we are examining a standing wave created in an organ pipe. The frequency of the sound produced by this standing wave is 300 Hz. Our goal is to determine the fundamental frequency of the organ pipe.
**Question:** What is the fundamental frequency of the organ pipe?
*Hint: Work in variables first and then plug in numbers only at the very end.*
![Standing Wave]
**Explanation of Diagram:**
The diagram shows a standing wave pattern within an organ pipe. The wave pattern illustrates three complete wavelengths fitting inside the length of the organ pipe, indicating that this is a higher harmonic.
**Possible Answers:**
- **150 Hz**
- **100 Hz**
- **60 Hz**
- **300 Hz**
- **68.6 Hz**
To approach this problem, follow these steps:
1. Identify the harmonic number (n) from the diagram.
2. Use the relationship between the frequency of the nth harmonic (f_n) and the fundamental frequency (f_1): \( f_n = n \cdot f_1 \).
3. Rearrange to solve for the fundamental frequency: \( f_1 = \frac{f_n}{n} \).
4. Plug in the given values to find the fundamental frequency.
Let's calculate:
Given \( f_n = 300 \) Hz and observing 3 complete wavelengths, n = 3.
So, the fundamental frequency \( f_1 \) is:
\[ f_1 = \frac{300 \text{ Hz}}{3} = 100 \text{ Hz} \]
Therefore, the fundamental frequency of the organ pipe is **100 Hz**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91195c14-8c67-42a0-b9d0-a3e8c2a59df0%2F9d990f54-fb6c-40fa-9262-58bf4e8fe587%2F7uhptd2.png&w=3840&q=75)
Transcribed Image Text:**Understanding Standing Waves in Organ Pipes**
In this example, we are examining a standing wave created in an organ pipe. The frequency of the sound produced by this standing wave is 300 Hz. Our goal is to determine the fundamental frequency of the organ pipe.
**Question:** What is the fundamental frequency of the organ pipe?
*Hint: Work in variables first and then plug in numbers only at the very end.*
![Standing Wave]
**Explanation of Diagram:**
The diagram shows a standing wave pattern within an organ pipe. The wave pattern illustrates three complete wavelengths fitting inside the length of the organ pipe, indicating that this is a higher harmonic.
**Possible Answers:**
- **150 Hz**
- **100 Hz**
- **60 Hz**
- **300 Hz**
- **68.6 Hz**
To approach this problem, follow these steps:
1. Identify the harmonic number (n) from the diagram.
2. Use the relationship between the frequency of the nth harmonic (f_n) and the fundamental frequency (f_1): \( f_n = n \cdot f_1 \).
3. Rearrange to solve for the fundamental frequency: \( f_1 = \frac{f_n}{n} \).
4. Plug in the given values to find the fundamental frequency.
Let's calculate:
Given \( f_n = 300 \) Hz and observing 3 complete wavelengths, n = 3.
So, the fundamental frequency \( f_1 \) is:
\[ f_1 = \frac{300 \text{ Hz}}{3} = 100 \text{ Hz} \]
Therefore, the fundamental frequency of the organ pipe is **100 Hz**.
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