aka Factors affecting the amplitude of sound propagating through a tube

Presentation slides

Detailed research report

Motivation
Human beings are sensitive to sound. Sounds come from different sources. Some sounds, such as from a flute, are desirable and may need amplification. Others, such as from a car exhaust pipe, may need attenuation. Many of these sounds propagate through a tube. Identifying methods to amplify desirable sounds and attenuate noise is important for human comfort. Sound propagates in waves with different frequencies, and that desirable sounds and noise have different frequencies. Also, sound waves can interfere with each other either constructively, causing the sound level to increase, or destructively, resulting in overall sound level reduction. Further, sound propagating through a tube can undergo reflections at its open ends and reflected sounds can interfere resulting in overall amplitude increase or reduction.

Goal
The objective of this experiment is to determine how a change in length of the tube affects the amplitude of sound propagating through it.

Hypothesis
The hypothesis is that sound amplitude will periodically increase and decrease as the length of the tube is reduced.

Materials and Procedure
Sound generated with a sound generator app on an iPhone is propagated through an adjustable-length cardboard tube. The amplitude at the end of the tube is measured in decibels using another app on another iPhone and a microphone. The length of the tube is decreased while recording the lengths and amplitudes at which the sound amplitude minimums and maximums occur.

Results
As the tube length is decreased, the sound amplitude increases and decreases and increases again, thus confirming the hypothesis. The amplitude of sound oscillates as the length of the tube is decreased. Also, the difference between the lengths of the tube at which consecutive amplitude extrema occur is almost constant for a given frequency. This difference decreases as the frequency of sound increases. The maximum variation in amplitude is almost constant for a given frequency. Finally, the maximum variation in amplitude decreases as the frequency of sound increases.

Conclusion
The results confirm the hypothesis. As the length of the tube is decreased, the amplitude oscillates between a maximum and a minimum. For a given tube length, some frequencies can reach a maximum amplitude while some others can reach a minimum. Therefore, the results can be used to identify certain combinations of frequencies and tube lengths to attenuate undesired frequencies or amplify desired frequencies. Real world applications include reducing undesirable noise from car exhaust and noise cancellation in headphones.