Optional Practical: Resonance in a bucket

Introduction

In this practical water waves in a shallow rectangular container will be investigated. Pour about 1cm depth of water into the container and place it on the table. Push the side of the container and you will see a wave travel across the surface. The wave will travel to the opposite side of the container and reflect back. If you time the pushes correctly you can keep the wave bouncing backwards and forwards across the container, this is an example of resonance.

Research question

What is the relationship between the velocity of water waves and the depth of water?

Independent variable: Depth
Dependent variable: Velocity
Controlled variables: properties of water, area of container.

Theory

The theory of water waves is rather complicated (you can read the details here ) but it can be shown that if the water is shallow the velocity,v depends upon the acceleration due to gravity,g and the depth,d according to the following equation:

v=√ gd 

(This is an approximation for waves where the wavelength is much bigger than the depth.)

Method

By sending waves back and forwards across the container measure the velocity of the waves for different depths of water. Then, using a graphical method show that v=√ gd    and find a value for g.

New Waves in a bucket 

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