1. Resonant Frequency of a Closed Tube
The fundamental resonant frequency (the lowest frequency that resonates) of a closed tube is given by:
* f = v / (4L)
Where:
* f is the resonant frequency
* v is the speed of sound in air (approximately 343 m/s at room temperature)
* L is the length of the tube
2. Calculation for the Empty Bottle
* L = 18 cm = 0.18 m
* f = 343 m/s / (4 * 0.18 m) ≈ 476 Hz
So, the fundamental resonant frequency of the empty soda bottle is approximately 476 Hz.
3. Effect of Filling the Bottle
When you fill the bottle with liquid, the effective length of the air column that vibrates changes. The air column now only extends from the top of the liquid to the top of the bottle.
* New L = (1/3) * 18 cm = 6 cm = 0.06 m (Since it's one-third full)
* New f = 343 m/s / (4 * 0.06 m) ≈ 1429 Hz
The resonant frequency increases to approximately 1429 Hz when the bottle is one-third full.
Important Note:
* This calculation assumes that the speed of sound in air remains constant. In reality, the speed of sound can be affected by temperature and humidity.
* This is a simplified model. The actual resonant frequencies of a real soda bottle will be more complex due to factors like the shape of the bottle and the presence of the opening.
In summary, filling the soda bottle with liquid shortens the effective air column length, leading to a higher resonant frequency.
