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## National STEM Learning Centre

Skip to 0 minutes and 6 seconds [Sand Bucket] Another investigation that students can perform uses a swinging bucket containing sand. When paper is pulled underneath at a constant rate, a sine wave is described by the sand on the paper. To enable the sand to flow freely and give a recognisable trace on the paper, a 1cm diameter hole has been cut in the bottom of the bucket. The level of the sand in the bucket needs to be reasonably high to allow it to flow through. The frequency of the wave is changed by altering the length of the string. A-level students should be able to calculate the period of the bucket by knowing the length of the string. By pulling the paper more quickly, this will increase the wavelength.

Skip to 0 minutes and 54 seconds If the frequency is constant, we can see from the wave equation that if the speed increases, then the wavelength must also increase.

# Sand and swinging bucket

This practical requires some testing to get it working well, but it can be used to investigate the wave equation.

The hole in the bucket needs to be large enough to allow the flow of sand through the bucket without getting stuck, but not too big that the sand falls out too quickly. A hole of around 1cm diameter is good.

Varying the length of the string will allow you to vary the frequency, which can be calculated from the inverse of the period on one oscillation.

When pulling the paper underneath the sand, it is important to try to keep the speed fairly constant for a particular run, so that the wavelength described by the sand on the paper remains constant. Perhaps this could be achieved by using a robot to pull the paper, bearing in mind that the weight in tow will change as the sand falls from the bucket.

This experiment is also useful at Advanced Level to link simple harmonic motion to waves. At A-level, the frequency could also be calculated using the length of the string and the gravitational constant, g.

Let us know if you have any tips for this practical, and how you might use it in the classroom.