4.9.10 Determining the Speed of Sound in Air in a Resonance Tube

Aims of the Experiment

• The aim of the experiment is calculate the speed of sound in air using a tuning fork and a tube of water

• Independent variable = Air level in the tube
• Dependent variable = Length of the air column in the tube where resonance occurs, L
• Control variables:
  • Temperature of the water
  • Frequency of the tuning fork

Equipment List

Method

Apparatus setup to measure the speed of sound in a column of air

1. Set up the equipment and fill up the beaker halfway with water
2. Place the tube inside the beaker, so the water comes up a quarter of the way. The side of the tube in the water acts as a closed-end
3. Hold the tuning fork above the open end of the tube and strike it lightly with the small hammer
4. Slowly lower the tube into the water by loosening the clamp until the intensity of sound is amplified
5. When resonance (loudest sound) is heard, mark the water level with a rubber band or marker pen. Record this as L₁
6. Then, lower the water further until the next point of resonance is heard and mark it. Record this as L₂
7. Keep going in this manner as far as possible

Analysis of Results

Standing waves in the air columns are used to calculate the wavelength of the sound waves

• Resonance should occur when the open tube length L is equal to λ / 4, 3λ / 4 and 5λ / 4
  • The loudness of the sound in the tube from the fork will be small at the node of the sound wave
  • The sound will be the loudest at the antinode of the sound wave

• At L₁ the wavelength is λ / 4
• At L₂ the wavelength is 3λ / 4

L₂ – L₁ = λ / 2

• Therefore, the wavelength of the sound λ is equal to:

λ = 2(L₂ – L₁)

• Another value of λ could also be found from the distance between L₃ and L₂ and a mean wavelength can be calculated
• From the wave equation:

v = fλ

• The speed of the sound wave, v, can found from the product of the frequency f of the tuning fork and the wavelength λ calculated

Evaluating the Experiment

Systematic Errors:

• The tuning fork should be struck at the same place above the tube each time
• The tuning fork should be struck with the same force each time

• Make sure the marker is a thin line to get a more accurate reading of the water level
• Submerge the tube into the water slowly, so the antinode of the sound wave (loudest sound) is not missed
• Repeat the experiment to record more reliable readings, since the point where the sound is the loudest is subjective
• Using a resonance tube with a scale will help account for error when measuring the length of the air column within it

Safety Considerations

• Don't let the tuning fork touch the tube, since the vibrations could break or crack it
• Make sure the water is at room temperature, and not too hot or cold
• Make sure no electrical equipment is near the water, otherwise they could be damaged