with Math and Measurement

Welcome to Phil and Sarah's page on making homemade musical instruments — where common household items are transformed into musical marvels using math and measurement!  Specifically, we'll cover how musical instruments vibrate in a series of fractions called the harmonic series, explain how to design your own homemade musical instruments by measuring length and liquid volume, and demonstrate how to play rhythmic patterns in a homemade percussion band.

 The garden hose plays the harmonic series.

Harmonic Series

Instruments vibrate in fractions: Many instruments produce sound by vibrating a column of air inside a tube, e.g. flute, trumpet, and saxophone.  As waves of air move inside a tube, they vibrate in wholes, halves, thirds, fourths, and fifths — fractions in the harmonic series.   This series of harmonics can be played on a garden hose trumpet, a Whirly-tube, sports bottle straw, as well as any homemade flute or bugle.   Phil's daughter, Sarah, demonstrates exactly how this vibrating column of air looks and sounds with her multimedia activity on the harmonic series.  She also shows how these fractions, or harmonics, are produced with string instruments such as a violin or a guitar.  In addition, you will see the scientific properties for each wave, and hear the sounds of each harmonic on a violin (string), pan pipes (closed-end tube), and with her trumpet (open-end tube).  While you're there, be sure to check out the bugle calls!

Length

Shorter is Higher — Longer is Lower: Taking it a step further, students can change the length of this vibrating column of air by varying the length of a tube.  As a tube gets shorter, it produces a higher pitch or frequency.  This happens because sound waves can travel, or vibrate, a shorter distance faster than a longer distance.  To see and hear how this works, check out Phil and Sarah's instrument making activities on didgeritubes, panpipes, melodic tube drums, and musical fraction tubes.  These four activities allow students to change pitch by changing the length of a vibrating column of air inside a tube.

 Didgeritubes! (with Science Olympiad Update!) Pan Pipes or Pan Flute (with Science Olympiad Update!) Melodic Tube Drums (with Science Olympiad Update!) Musical Fraction Tubes

The tubular glockenspiel below, also varies pitch with longer and shorter tubes.  However, this time, the pitch is not produced by a vibrating column of air.  Instead, it is produced by vibrating the substance of the instrument itself – in this case, the metal tubingThe same principal applies: longer is lower, and shorter is faster.

 Less water is higher — more water is lower.

Liquid Volume

Less is Higher — More is Lower: Students can change weight/mass by measuring liquid volume.  When water is added to a bottle, the pitch or frequency gets lower.  This happens because as students add water, they also add more mass to the bottle — the combined mass of the bottle plus the added water.  As with the tubular glockenspiel, more mass results in a slower/lower vibrating frequency, and less mass produces a faster/higher vibrating frequency.   To see and hear how this works, check out Phil and Sarah's instrument making activity on a water bottle xylophone.  This activity allows students to change pitch by changing the mass of a bottle.