When everyone else is out of her classroom, Amy takes over and does some quite amazing experiments. She specializes in discrepant events. Watch and try to predict what will happen. Expect to be quite amazed.

This month, Amy investigates the Bottle Bandwidth Paradox.

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Materials
four identical glass bottles
water
food coloring (optional)
rod to tap glass
safety glasses

Procedure
1. Fill each of the four bottles with different levels of water. Fill one almost to the top. Make another three-quarters full. Another should be half full. The fourth should be nearly empty. If desired, tint the water with a few drops of food coloring so that everyone can see it clearly.
2. Blow across the top of each bottle. Note the pitch of the sound.
3. Tap the side of the each bottle with the rod. Note the pitch of the sound.

Background
When blowing across the top of the bottles, you found that the bottle with the least water had the lowest pitch. The one with the most water had the highest pitch. When tapping the bottles, the opposite was true.

The pitch of sound is determined by the frequency (speed) of the sound waves detected by the ear. The higher the frequency, the higher the pitch.

When blowing across the top of the bottle, the column of air trapped inside the bottle begins to vibrate. The longer the column of air, the more room the sound waves have to decrease their speed. The longest column of air was in the bottle with the least water. Therefore, it had the lowest pitch (slowest frequency). The shortest column of air was in the bottle with the most water. Therefore, it had the highest pitch (fastest frequency).

When tapping the side of the bottle, the vibration occurs in the combined mass of the bottle plus the water inside. The greater the combined mass, the more room the sound waves have to be absorbed and slowed. The greatest combined mass was in the bottle with the most water. Therefore, it had the lowest pitch (slowest frequency). The lowest combined mass was in the bottle with the least water. Therefore, it had the highest pitch (fastest frequency).

To extend the investigation, try varying the length of the air column using a plastic straw. Use your finger to block one end and blow across the open end. Then, systematically reduce the length of the column of air inside the straw by placing it in a glass of water an inch or so at a time. As the column of air gets shorter, the pitch gets higher.