A)For a closed air column, the length of the air column, L for the first resonant length is
L = λ/4
where
λ = wavelength
From the information given,
L = 60 cm
We would convert 60 cm to m. Recall, 100 cm = 1 m
60 cm = 60/100 = 0.6 m
speed of sound, v = 344
By substituting L = 0.6 into L = λ/4
, we have
0.6 = λ/4
λ = 4 * 0.6 = 2.4
recall, frequency, f = v/λ
where
λ = wavelength
v = velocity
f = frequency
Thus,
f = 344/2.4
f = 143.33 Hz
The frequency at the first resonant length is 143.33 Hz
B) For a closed air column, the length of the air column, L for the second resonant length is
L = 3λ/4
0.6 = 3λ/4
0.6 x 4 = 3λ
λ = (0.6 x 4)/3 = 0.8
f = 344/0.8
f = 430 Hz
The frequency at the second resonant length is 430 Hz
C) For a closed air column, the length of the air column, L for the third resonant length is
L = 5λ/4
0.6 = 5λ/4
0.6 x 4 = 5λ
λ = (0.6 x 4)/5 = 0.48
f = 344/0.48
f = 716.7 Hz
The frequency at the third resonant length is 716.7 Hz