The sound of a bottle
Measuring the speed of sound by uncorking a bottle of wine
Author:
Title 4
Learning objectives :
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.
Concepts covered
Helmholtz resonance; Sound waves; Fundamental frequency; Acoustic cavities; Speed of sound
What students will do :
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.
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
Scientific background :
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.