5-4: 1 SEE ANSWER

Answer: 75.6 cm and 71.9 cm

First, find the effective lengths using the formula for an open cylindrical tube and the values given in the question:

    fn = n X (10.05/ Leff) X (square root of (Ta))
    220 Hz = n X (10.05/ Leff) X (square root of 295K)
    220 Hz = n X (10.05/ Leff) X (17.19)
    220 Hz = n X (172.6/ Leff)
    Leff = n (172.6/220 Hz)
    Leff = n 0.78m

Now, use the effective length to find the actual length using the formula for the actual length of an open cylindrical tube:

    For a tube with radius 2 centimeters:
    Lact = Leff - 1.226R
    Lact = 0.78m - 1.226 (0.02m)
    Lact = 0.756m = 75.6 cm

    For a tube with radius 5 centimeters:
    Lact = Leff - 1.226R
    Lact = 0l78m - 1.226 (0.05m
    Lact = 0.719m = 71.9cm

The tubes with radii 2 cm and 5 cm would have the actual lengths of 75.6 cm and 71.9 cm, respectively.

REDIRECT 5-4 Vibrational Mode of an Air Column