Final answer:
The wavelength of the second overtone in a tube open at one end is found using the formula λ₃ = 4L/5, where L is the length of the tube and λ₃ represents the wavelength of the second overtone.
Step-by-step explanation:
To find the wavelength of the second overtone in a tube that is open at one end and closed at the other, we first understand that the resonant wavelengths in such a tube are determined by odd multiples of the fundamental frequency's wavelength. The fundamental wavelength (λ₁) equals 4L in such a tube. The first overtone has a wavelength of 4L/3, and each subsequent overtone has a shorter wavelength, being determined by the formula λ = 4L/n, where n is an odd integer representing the number of quarter wavelengths that fit into the tube's length.
For the second overtone, n would be 5 since this is the next odd integer after 3 (which was for the first overtone). Thus, the equation to find the wavelength (λ₃) of the second overtone would be λ₃ = 4L/5, where L is the length of the tube.