IB Physics Practical - Stubbiephone Wind Band

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Physics

IB Physics Practical Assessment

Skill 1: Planning (Part A and Part B)

Stubbiephone Wind Band

The music department of a school is in need of an instrument that covers a range of one octave (eight notes). Such an instrument, however, cannot be purchased due to the shrinking budget of the department and a hand made alternative needs to be produced. It has been decided that the instrument will be made up of eight short and fat beer bottles because beer bottles are cheap and readily available. This report contains a plan for an experiment to investigate how these bottles can be made to produce the eight notes required to form an octave.

PART ONE - PREDICTION

The shape of a beer bottle can be compared to that of a closed pipe, with one end of the bottle open, the mouth, and the other end closed. When we blow over the mouth of a beer bottle, a sound is produced. It is known that sound travels through a closed pipe in the form of a standing wave, with the node at the closed end (bottom of the bottle) and the anti node near the opening of the bottle as in figure one(a). The length of the standing wave in a bottle is equivalent to the actual length of the bottle. Therefore, to vary the length of the standing wave will require the length of the bottle to be changed. One way to do this is to fill the bottle with water. Referring to figure one(b), we can see that when a bottle is filled with water, the length of the bottle is reduced from L to L2.

The frequency of a note (i.e. the pitch) is determined by the frequency of the standing wave. That is, if the frequency of the standing wave is of a high value, the pitch of the note will also be high and vice-versa. Therefore, different notes can be achieved using the beer bottles by varying the frequency of the standing wave. It is known that frequency varies with the length of the standing wave. Therefore, by investigating the relationship between the length and the frequency a formula can be deduced. This formula can be used to work out how we can vary the length of the standing wave in the beer bottle (i.e. changing the amount of water inside it) to get the eight notes required to form an octave.
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If we look at the illustration of a standing wave (figure two) in a closed pipe, it can be seen that the length of a standing wave is a quarter of a wavelength. This can be represented algebraically as:

L = ?/4

A formula relating frequency, speed of sound and wavelength is:

f = V/?

If we combine these two formulas together we get an algebraic representation of the relationship between frequency and the speed of sound and length of a standing wave at First harmonic:

f1 = V/4L

From further observation, ...

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