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Resonance in a bucket

Aims

  • Enhance the concept of a wave as a transfer of energy.
  • Revise definition of velocity.
  • See the effect of water depth on wave speed.
  • Hands on example of resonance.
  • Introduce standing waves.

Apparatus

This practical uses very simple apparatus, a plastic ice cream carton a ruler and a stop watch. The results are surprisingly good. Measuring the water depth is easier if you have a transparent box or you could supply a measuring cylinder (borrowed from chemistry) to measure the volume of water and calculate the depth knowing the side length of the box. I don't have any stop clocks but used an online version, students can also use their phones.

Common problems

Students always think that the speed of the wave is dependent on when they push the box, get then to try to repeat the same depth several times and they will find out that it isn't, it's like pushing a swing. It might also be interesting to point out that although this is an oscillation it is not SHM since the velocity is constant. Because of the oscillatory nature of the motion students get diverted into thinking about time period and frequency and forget that they are measuring wave velocity so need to measure the length of the box. Some boxes don't have a flat bottom so can cause a problem , it's also important to keep the box horizontal otherwise the velocity won't be constant. Waves with a big amplitude might also affect the velocity as the depth is reduced when all the water moves into the crest. When working in pairs a lot of student will have one count and the other press the button on the clock, it's better for one to do both.

Conclusion and Evaluation

Although the graph is quite linear the value for g tends to be quite low. Measurements are reasonably accurate and error bars small so the main reason is probably because equation given is an approximation, however students are always very eager to blame experimental errors for their result. This can lead to a discussion about whether there is any use for an equation that gives such an approximate result. The nature of the wave is also important so although the equation works well for waves in the sea it might not apply so well to waves in a bucket.

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