Tube effect
Measuring the speed of sound with a tube
Author:
Title 4
Learning objectives :
This activity allows students to measure the speed of sound by analyzing the resonant frequencies of a tube. It illustrates how resonance phenomena can be used to determine physical constants.
Concepts covered
Acoustic resonance; Natural frequencies; Spectral analysis; Standing waves; Sound propagation
What students will do :
The student generates white noise with a smartphone placed at the entrance of a cylindrical tube then uses a second smartphone with FizziQ to analyze the spectrum of frequencies amplified by resonance. By identifying amplitude peaks in the spectrum and applying the resonance formula for an open tube the student can calculate the speed of sound and compare its value to standard references.
What is required :
Two smartphones with the FizziQ application; A cylindrical tube (roll of toilet paper cardboard or other); A tape measure to measure the dimensions of the tube; FizziQ experience notebook
Scientific background :
When white noise (containing all frequencies at equal intensity) is emitted at the input of a tube, the frequencies which correspond to the natural resonance modes of the tube are amplified by resonance. For a tube open at both ends, the resonant frequencies are given by the formula: f = n×c/(2L+1.24D), where n is an integer (1,2,3,...) representing the mode, c is the speed of sound, L is the length of the tube, and D its diameter. The corrective term 1.24D takes into account the edge effect at the end of the tube (the pressure belly does not form exactly at the opening but slightly beyond). FizziQ's frequency spectrum uses a fast Fourier transform (FFT) to decompose the sound signal picked up by the microphone and display its frequency content. The observed peaks correspond to the harmonics of the fundamental frequency. By precisely measuring these frequencies, the length and the diameter of the tube, we can calculate the speed of sound: c = (2L+1.24D)×f₁, where f₁ is the fundamental frequency (first peak). The theoretical speed of sound in air at 20°C is approximately 343 m/s, but varies with temperature according to: c = 331.3 + 0.606×T (T in °C). This experiment makes it possible to obtain a measurement with a precision of around ±2%.