The resonant wavelengths of a closed glass tube follow a pattern where each successive resonant wavelength is equal to four times the length of the tube divided by an odd integer. Mathematically, we can express it as:
λ = (4L) / n
where λ represents the wavelength, L is the length of the tube, and n is the mode number (1, 3, 5, etc.).
In this case, we are given the first resonant wavelength, which is 24 cm. Therefore, we can set up the equation as follows:
24 cm = (4L) / 1
To find the length of the tube (L), we rearrange the equation:
L = (24 cm * 1) / 4
L = 6 cm
Thus, the length of the glass tube is 6 cm.