Lab handout FYI

Harmonics on a string

A special area of wave physics involves "harmonics on a string."  Harmonics arise due to reflected waves interfering with incoming waves.  At the right frequencies, resonance occurs - so, the "standing wave" can get a pretty big amplitude with minimal energy input.  This phenomenon is a lot like pumping the swings to make yourself go higher.  In general, a string has a lowest possible frequency (the "resonant frequency") at which it will vibrate naturally - imagine plucking a string and hearing the note that results.  However, there are other frequencies ("harmonics") that can be produced that will also cause familiar wave patterns.  That's what today's lab is all about.

In this lab, you will determine the relationships relevant for harmonics on a string.  First, some definitions:

harmonic number, n

- this is the number of "humps" or "half-waves" present on a string.  The sequence starts at 1 and goes up higher and higher (by integers) until the string doesn't exhibit much wave motion to the naked eye (though indeed there may still be harmonics)

wavelength, lambda (l)

- literally, the size of a complete wave.  Crest-to-crest or trough-to-trough distance.  Could also be the distance between any 2 points in phase with each other

frequency, f

- the number of waves or vibrations or oscillations per second

wave speed, v

- the rate at which the wave energy travels.  Could conceivably be measured with a stopwatch, but is better computed with the equation:  v = f l

Procedure

Set up a wave oscillator apparatus, with a pulley attached to a table.  Your string will be draped over the pulley.  Make sure the string is firmly attached to the oscillator and a weight is attached to the end of the string.

Measure the effective length of the string:  from oscillator to top of pulley.  Also measure the hanging mass.

Part I

1.  Starting very low, find the lowest possible frequency (on the sine wave generator) that gives you an n=1 (lowest) harmonic -- this is ONE hump.  Record frequency.

2.  Gradually increase the frequency, advancing through a series of harmonics.  Record n and f.  Do as many harmonics as you can. 

3.  In a table, record n, f, l and v.  You will need to calculate l and v.

Determine trends worth noting.

Part II

Chat with other groups – those who used a different hanging mass.  See if you can determine if there are differences due to the weight that hangs (and provides tension in the string).

Questions

1.  What seems to be clear from your data in part I?

2.  What seems to be clear from your data in part II?

3.  You may not play a stringed instrument, but what can you infer from your experiment as it relates to guitars, violins, etc.?

4.  Write a general conclusion – things you learned, things that were interesting, sources of error (threats to validity), suggestions for improving the experiment, and so forth.

Your complete lab report should include:  a title, date(s) performed, lab partner(s), purpose of lab (at the beginning), data, graphs (if relevant), pictures (if helpful), sample calculation (though all calculations will be done), conclusion and answers to questions.