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 effective length of 0.403 m. Take 343 m/s for the speed of sound inside the instrument. wavelength: frequency: Hz

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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.
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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