Answer:
1) λ = 24.7 cm, 2) f = 13.88 Hz, 3) L = 117.3 cm
Explanation:
1) This is a resonance process, that is, the wave going downwards will interfere with the wave going upwards.
This is a tube with one end closed and the other open, at the closed end there is a node and at the open end a belly, so the resonances are
L = λ / 4
λ = 4L 1st harmonic
λ = 4L / 3 third harmonic
λ = 4L / 5 fifth harmonic
λ = 4L / n ’ n’ odd number n ’= (2n +1)
the wavelength is requested for the eighth resonance n = 8, the corresponding prime number is
n ’= 2 8 +1
n ’= 17
we substitute
λ = 4 105/17
λ = 24.7 cm
2) the speed of the wave is related to the wavelength and frequency
v = λf
f = v /λ
f = 343 / 24.7
f = 13.88 Hz
3) the next resonance occurs for n = 9, so the prime number is
n ’= 2 9 +1
n ’= 19
L = n’ λ / 4
L = 19 λ / 4
We must suppose a value for the wavelength, if the wavelength is present in the tube and the length of the column increases, the resonance number increases
L = 19 24.7/4
L = 117.3 cm