Answer :
Final answer:
The wavelength of the third normal mode of vibration of a clarinet's air column with an effective length of 38.1 cm is 0.762 m, and the frequency is 454.8 Hz.
Explanation:
In a clarinet, the third normal mode of vibration of the air column has three antinodes, which means it has three segments of compression and rarefaction. Each segment corresponds to half of a wavelength. So, the total wavelength for the third mode is twice the effective length of the clarinet's air column.
Given that the effective length of the clarinet's air column is 38.1 cm and the speed of sound inside the instrument is 346 m/s, we can calculate the wavelength using the formula:
Wavelength = 2 * Length
Substituting the values, we get:
Wavelength = 2 * 0.381 m = 0.762 m
The frequency can be calculated using the formula:
Frequency = Speed of Sound / Wavelength
Substituting the values, we get:
Frequency = 346 m/s / 0.762 m = 454.8 Hz
