Answer:
The height of the water column = 1.62405[tex]\overline{30}[/tex] × 10⁻¹ m
Explanation:
The air cavity in the Coke bottle = 0.220 m deep
The fundamental (frequency) it plays when water is added to shorten the column and it is blown across the top, f = 528 Hz
The given speed of sound in air, v = 343 m/s
We note that the air cavity in the coke bottle is equivalent to a tube closed at one end
The fundamental frequency for a tube closed at one end, 'f', is given as follows;
f = v/(4·L) = v/λ
Where;
L = The height of the water column
λ = The wavelength of the wave
∴ 4·L = v/f = (343 m/s)/(528 Hz) = 0.6496[tex]\overline{21}[/tex] m
∴ L = 0.6496[tex]\overline{21}[/tex] m/4 = 0.162405[tex]\overline{30}[/tex] m
The height of the water column = 1.62405[tex]\overline{30}[/tex] × 10⁻¹ m.
