Helmholtz
Measuring the speed of sound using a test tube
Author:
Title 4
Learning objectives :
This activity allows students to measure the speed of sound using acoustic resonance in a tube. It illustrates how vibrational phenomena can be used to determine fundamental physical constants.
Concepts covered
Acoustic resonance; Standing waves; Fundamental frequency; Helmholtz resonator; Vibration of air columns
What students will do :
The student blows on the edge of a test tube to produce a sound and measures the fundamental frequency emitted with FizziQ. By modifying the length of the air column by partially filling the test tube with water and applying the resonance formula for a closed tube the student calculates the speed of sound and compares its value to the theoretical value.
What is required :
Smartphone with the FizziQ application; A graduated cylinder or similar tube; Water to change the length of the air column; Meter or ruler to measure the dimensions of the tube; FizziQ experience notebook
Scientific background :
When we blow on the edge of a tube, we create an acoustic disturbance which excites the natural resonance modes of the air column contained in the tube. For a tube closed at one end (like a test tube), only standing waves with the pressure node at the closed end and the antinode at the open end can be established. The fundamental resonant frequency f₁ is given by the formula: f₁ = c/(4L+2.48D), where c is the speed of sound, L the effective length of the air column, and D the diameter of the tube. The corrective term 2.48D takes into account the edge effect at the opening: the sound wave does not stop exactly at the end of the tube but extends slightly beyond. Hermann von Helmholtz (1821-1894) studied these acoustic resonance phenomena in detail in the 19th century. By precisely measuring the length L, the diameter D and the frequency f₁, we can calculate the speed of sound: c = f₁(4L+2.48D). This value depends on the temperature T according to the relationship c = 331.3 + 0.606T (with T in °C), or approximately 343 m/s at 20°C. By adding water to the test tube, the length L of the air column is reduced, thus increasing the fundamental frequency. This inverse relationship between length and frequency confirms the theory of standing waves. FizziQ's Fundamental Frequency tool uses the Fourier transform to determine the dominant frequency of the emitted sound, allowing precise measurement of f₁.