The sound of a bottle

This activity allows students to determine the speed of sound by analyzing the resonance phenomenon when opening a bottle. It connects physical acoustics and everyday experiences.

The satisfying pop of a wine bottle being uncorked is more than just a festive sound; it is a miniature physics experiment in Helmholtz resonance. Hermann von Helmholtz, the 19th-century German physicist, studied how enclosed air cavities with narrow openings vibrate at specific natural frequencies. The wine bottle, with its large body and narrow neck, is a textbook Helmholtz resonator. When the cork is suddenly removed, the compressed air in the neck rushes out, creating an acoustic disturbance that excites the air column into oscillation at its resonant frequency. This frequency depends on the neck geometry and the volume of the cavity in a precise mathematical way. By measuring the pop frequency with FizziQ and knowing the bottle's dimensions, students can work backward to calculate the speed of sound, turning a convivial moment into a rigorous physics measurement.

Learning objectives:

The student records and analyzes the sound produced when opening a bottle of wine using the FizziQ Fundamental Frequency tool. By measuring the frequency of the characteristic 'pop' and knowing the dimensions of the neck, the student applies the Helmholtz resonance formula to calculate the speed of sound.

Level:

High school

FizziQ

Author:

Duration (minutes) :

30

What students will do :

- Record and analyze the sound produced when uncorking a bottle using FizziQ
- Measure the fundamental frequency of the resonant pop
- Apply the Helmholtz resonator formula to calculate the speed of sound from the measured frequency and bottle dimensions
- Compare the calculated speed of sound with the accepted value
- Understand the physics of Helmholtz resonance and acoustic cavities

Scientific concepts:

- Helmholtz resonance
- Sound waves
- Fundamental frequency
- Acoustic cavities
- Speed of sound

Sensors:

- Microphone (frequency meter / fundamental frequency measurement)
- FizziQ spectrum analyzer

What is required:

- Smartphone with the FizziQ application
- A bottle of wine (with an adult)
- Optional: a recorder to repeat the analysis
- Meter or ruler to measure the dimensions of the neck
- FizziQ experience notebook

Experimental procedure:

Measure the dimensions of the bottle neck: length L (depth of the neck) and internal diameter D of the opening. Also estimate the volume V of the air cavity inside the bottle.
Open FizziQ and select the Frequency Meter (fundamental frequency) tool.
Hold the smartphone close to the bottle opening (within 10-15 cm).
Start recording, then uncork the bottle with a quick, firm pull. (This must be done with adult supervision.)
The frequency meter should capture the resonant frequency of the pop. Record this value as f.
If the reading was too brief, try using the Spectrum Analyzer mode and replay the recording to identify the dominant frequency peak.
Repeat the measurement with 2-3 bottles of the same type for consistency.
Calculate the cross-sectional area of the neck: A = π(D/2)².
Apply the Helmholtz resonator formula: f = (c / 2π) × √(A / (V × L_eff)), where L_eff = L + 0.6D is the effective neck length including end correction.
Rearrange to solve for the speed of sound: c = 2πf × √(V × L_eff / A).
Calculate c and compare with the accepted value of approximately 343 m/s at 20°C.
Discuss the sources of uncertainty: volume estimation, neck dimension measurement, and frequency measurement precision.

Expected results:

The pop frequency typically falls in the range of 300-600 Hz depending on the bottle shape and size. A standard 750 mL wine bottle with a neck length of about 8 cm and diameter of 2 cm produces a resonance around 400-500 Hz. The calculated speed of sound should fall within 300-380 m/s, with deviations from 343 m/s primarily due to the difficulty of accurately measuring the bottle's internal volume and neck dimensions. The end correction factor (0.6D) is important: without it, the calculated speed of sound will be systematically too high. Students should achieve agreement within 10-15% of the accepted value with careful measurements.

Scientific questions:

- What is a Helmholtz resonator, and how does it differ from a simple tube resonator?
- Why does the pop frequency depend on the volume of the bottle cavity?
- How would the resonant frequency change if you partially filled the bottle with water (reducing the air volume)?
- Why is the end correction (0.6D) necessary in the formula?
- What other everyday objects behave as Helmholtz resonators?
- How does temperature affect the speed of sound, and would this change your result?

Scientific explanations:

The characteristic 'pop' of a bottle being uncorked is a perfect example of a Helmholtz resonator, named after the German physicist Hermann von Helmholtz (1821-1894). This type of resonator consists of a cavity connected to the outside by a narrow opening, like the neck of a bottle.

The physical phenomenon occurs as follows: when the cork is removed quickly, the compressed air in the bottle suddenly escapes, creating an acoustic disturbance. This disturbance excites the column of air in the neck which begins to oscillate at its natural resonance frequency.

For a Helmholtz resonator, this frequency f is given by the formula: f = c/(4L+2.48D), where c is the speed of sound, L the length of the neck, and D its diameter. The 2.48D corrective term takes into account the acoustic radiation effect at the open end of the tube.

Typically, for a standard bottle of wine (neck 7-8 cm long and 2 cm in diameter), the frequency of the 'pop' is around 400-450 Hz. By precisely measuring this frequency with FizziQ and knowing the dimensions of the neck, we can reverse the formula to calculate the speed of sound: c = f×(4L+2.48D).

The theoretical speed of sound in air at 20°C is approximately 343 m/s, varying slightly with temperature according to the relationship c = 331.3 + 0.606×T (T in °C). This method generally provides an estimate with an accuracy of ±2-3%, depending on the clarity of the sound and the accuracy of the dimensional measurements.

Extension activities:

Frequently asked questions:

Q: The pop was too brief for the frequency meter to capture. What can I do?
R: Use the spectrum analyzer in recording mode and analyze the saved waveform afterward. The pop, though brief, contains enough cycles for spectral analysis. You can also blow across the bottle top to produce a sustained tone at approximately the same resonant frequency.

Q: How do I estimate the internal volume of the bottle?
R: Fill the bottle with water from a measuring cup and record the volume. For a standard 750 mL wine bottle, the air volume when empty is approximately 750 mL minus the neck volume.

Q: My calculated speed of sound is far from 343 m/s. What is the most likely source of error?
R: The volume estimation is usually the largest source of error. A 20% error in volume translates to about 10% error in the speed of sound. Measure the volume carefully using water.

Q: Can I use a beer bottle or soda bottle instead of a wine bottle?
R: Yes, any bottle with a distinct neck will work as a Helmholtz resonator. Measure its dimensions carefully and apply the same formula.