A tube is open at one end. If the fundamental frequency is created by a wavelength f, then which of the following describes the frequency and wavelength associated with the tube's fourth overtone?
The fundamental frequency of a tube open at one end corresponds to the first harmonic, where the wavelength is equal to four times the length of the tube.
The fourth overtone would correspond to the fourth harmonic. In an open tube, the wavelengths of the harmonics are determined by the formula:
λ = 2L/n
Where:
λ is the wavelength
L is the length of the tube
n is the harmonic number
For the fourth overtone (fourth harmonic), n = 4. Thus, the wavelength associated with the tube's fourth overtone is then:
λ = 2L/4 = L/2
So, the wavelength associated with the tube's fourth overtone is L/2 and the frequency can be determined by the equation:
f = v/λ
Where:
f is the frequency
v is the velocity of sound (assumed constant)
Since we are only interested in the relationship between frequencies and wavelengths, we can simply say that the frequency associated with the tube's fourth overtone is twice the frequency of the fundamental frequency.