Smart phones are expensive, but almost every student has one – everywhere in the world! Neither the school nor the teacher need to buy this powerful piece of equipment to use for physics lab. In this experiment, students use inexpensive cell phone Apps to generate tones and to measure frequency.
- Inexpensive cellphone Apps that work well:
- PitchLab, for tuning guitars, but here used for measuring frequency
- FG Tone Generator
- Test tubes: A variety of useful sizes are standard. 6″ (15 cm) tubes are easy to blow across to make a tone. The very large ones are a little bit difficult to blow for long enough to register the frequency. It is interesting to create tones from two tubes that differ in length by 2×, because these will produce pitches that are one octave apart — a factor of 2× in frequency.
- Graduated cylinder: A 100 mL cylinder can be filled to varying height with water, to show how the resonant frequency varies with air column length.
- Open cylinders or pipes: lengths 12″ to 18″ (~30 to 45 cm) produce resonances in a useful range. Metal tubes and pipes are readily available at low cost. It will be impossible to create sounds by blowing across the mouth of an open pipe. However, it is easy to calculate the expected resonance, and then use the tone generator to excite a good resonance. The air flow pattern and wavelength of the sound resonance may be easier to visualize in an open-end pipe than for the closed-end pipe such as a test tube (see below).
Resonant Air Flow
When the air in a test tube vibrates, the air motion must be a maximum at the mouth of the tube, and zero at the closed end. The air motion for the fundamental (lowest possible) frequency is a ‘breathing’ mode, as indicated in the figure: The distance between a node (zero motion at the left end) and the next consecutive antinode (maximum motion at the right open end) is 1/4 of the wavelength. Therefore a full wavelength is 4× the length of the test tube.
Air motion in an open tube ‘breathes’ symmetrically at both ends, so the fundamental resonance looks like: The distance between a node and the next consecutive antinode is 1/4 of the wavelength, so the full wavelength of the fundamental wavelength is 2× the length of the open tube.
Measuring speed of sound
I will be attaching videos here to demonstrate the open and closed tube resonances. The procedure for the closed tube is:
- Measure the length, L, of the tube in meters.
- Blow across the end of the tube and measure the frequency, f, of the tone using PitchLab or an equivalent App.
- Because the wavelength, λ = L/4, the speed of sound in air is:
c = f * λ = f * L/4
The procedure for the open tube is a little different:
- Measure the length, L, of the open tube in meters.
- Because the wavelength, λ = L/2, the fundamental frequency is: f = c/λ = 2 c/L. Use the known value of c ≈ 340 m/s
- Hold the little speaker of the your cell phone very near the end of the tube. Sweep the FG tone generator through a range of frequencies around the fundamental.
- When the tone gets very loud, that is the fundamental. Read the exact value, f1.
- How is sound resonance used in musical instruments?
Organ pipes, flutes, trumpets, guitars, etc., all use resonance to define the pitch of a note. The resonator can also play the part of an intermediary between the source and the room environment. Here are some pics of musical instruments that use resonators to enhance the volume of sound emanating from a vibration source. The source may be too small, or the vibration amplitude too small, to couple strongly to the air around the musical instrument. The resonator amplifies the vibrations.
- Higher harmonics
Try exciting higher harmonics in the tubes. The second harmonic in the open tube is f2 = 2 f1. The third harmonic is f3 = 3 f1. For the closed tube, the second harmonic is f2 = 3 f1. The third harmonic is f3 = 5 f1.