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![**Problem Statement:**
The clarinet is well-modeled as a cylindrical pipe that is open at one end and closed at the other. Find the wavelength and frequency of the third normal mode of vibration of a clarinet's air column with an effective length of 0.403 m. Take 343 m/s for the speed of sound inside the instrument.
**Input Fields:**
- **Wavelength:** ____ m
- **Frequency:** ____ Hz
**Instruction:**
To solve this problem, apply the formulae for a pipe open at one end:
1. **Wavelength** (\(\lambda\)) for the nth mode in a pipe that is open at one end and closed at the other is given by:
\[
\lambda_n = \frac{4L}{n}
\]
where \(n = 1, 3, 5, \ldots\) (odd harmonics only) and \(L\) is the length of the pipe.
2. **Frequency** (\(f\)) can be found using:
\[
f = \frac{v}{\lambda}
\]
where \(v\) is the speed of sound.
For the third mode (\(n=5\)), substitute the values and calculate both wavelength and frequency.](https://content.bartleby.com/qna-images/question/568ff014-20eb-4de5-8e14-1d7fe4707f89/e65f250a-b50e-44cb-90c3-c774dfc3b697/tawye9.jpeg)
Transcribed Image Text:**Problem Statement:**
The clarinet is well-modeled as a cylindrical pipe that is open at one end and closed at the other. Find the wavelength and frequency of the third normal mode of vibration of a clarinet's air column with an effective length of 0.403 m. Take 343 m/s for the speed of sound inside the instrument.
**Input Fields:**
- **Wavelength:** ____ m
- **Frequency:** ____ Hz
**Instruction:**
To solve this problem, apply the formulae for a pipe open at one end:
1. **Wavelength** (\(\lambda\)) for the nth mode in a pipe that is open at one end and closed at the other is given by:
\[
\lambda_n = \frac{4L}{n}
\]
where \(n = 1, 3, 5, \ldots\) (odd harmonics only) and \(L\) is the length of the pipe.
2. **Frequency** (\(f\)) can be found using:
\[
f = \frac{v}{\lambda}
\]
where \(v\) is the speed of sound.
For the third mode (\(n=5\)), substitute the values and calculate both wavelength and frequency.
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