**What it shows**:

The effect of length, tension, diameter, and kind of material on the pitch of a vibrating string is demonstrated. One may also show the harmonics of a vibrating string.

**How it works**:

The sonometer is a long hollow wooden box along the top of which are stretched one or more strings rigidly attached to the box at one end, with provision at the other for changing their tension. If there is just one string, it's known as a monochord. The monochord illustration is from John Tyndall's book entitled *Sound*, (Appleton, NY, 1867), and the sonometer is from J.A. Zahm's *Sound and Music*, (McClurg, Chicago, 1900).

These have been used for a long time as demonstration experiments. In fact, the monochord was invented in the 7th century B.C. by Pythagoras. The monochord was modified by the French instrument maker, Albert Marloye, in the mid 1800's and became known as a differential sonometer. Both monochord and sonometer are available for demonstrations. Several experiments are possible.

1) Show that the frequency varies inversely as the length of the vibrating string: The length of each string can be changed by moving a bridge under it. If the string is plucked near one end and stopped at 1/2, 1/3, 1/4, 1/5, etc, of its length, the 2nd, 3rd, 4th, 5th, etc. harmonics will be sounded. If a sharp-edged piece of soft rubber (an eraser) is used to stop the string, it is possible to make 10 or more harmonics audible.

2) Intervals: If you make the string 2/3 of its original length, the pitch rises exactly a perfect fifth, a fraction 3/2 above its original frequency. If you make the length 3/4 as long, the pitch rises a perfect fourth, or a fraction 4/3 above what it was.

3) The frequency varies directly as the square root of the tension: The string passes over a pulley and the tension is provided by hanging a weight from the end of the string ... quadruple the weight to secure twice the frequency.

4) Finally, the frequency varies inversely as the square root of the mass per unit length of the string. We have a small selection of wire sizes to show this.

**Setting it up**:

It's best to C-clamp the sonometer to the lecture bench or cart so that it doesn't slide around. A violin bow is also available if you wish to play a continuous tone rather than plucking the string.

**Comments**:

The ratios 2:1, 3:2, and 4:3 = 2 × 2:3 are considered to be the most consonant musical intervals. For this reason Pythagoras tried to build a musical scale with additional simple ratios. Unhappily, the scheme had serious limitations.