Respuesta :
Answer:
The fundamental frequency of the original tube is 159.169 Hz.
Explanation:
From the orientation of a wave in a tube open at both ends, we have at the fundamental frequency there is an anti-node at both ends.
Therefore the length of the tube = λ/2
and we have v = fλ where v = speed of sound in air = 343 m / s
f = frequency, therefore
Therefore λ = v/f = 343/416 = 0.824 m, therefore the tube opened at both ends is
λ/2 or 0.824/2 m = 0.4123 m long
The other tube with one end open we have a node at the closed end and an anti-node at the opened end which gives a fundamental frequency with the wavelength = λ/4
Therefore from v = fλ we have λ = v/f = 343/678 = 0.5059 m
Therefore the length of the tube = λ/4 = 0.5059÷4 = 0.1265 m
The length of the original tube is then given by the sum of the lengths of the two split tubes, that is =0.1265 + 0.4123 = 0.5387 m
Note that when combined the original tube still has only one end opened
Therefore the length of the tube = λ/4 or the wavelength = 4×0.5387
λ = 2.1549 m
Therefore we have f =v/λ = 343/2.1549
Frequency, f = 159.169 Hz
