Sonometers
   A Sonometer is a device for demonstrating the relationship between the frequency of the sound produced by a plucked string, and the tension, length and mass per unit length of the string. These relationships are usually called Mersenne's laws after Marin Mersenne (1588-1648), who investigated and codified them. For small amplitude vibration, the frequency is proportional to:

   a. the square root of the tension of the string,

   b. the reciprocal of the square root of the linear density of the string, 

   c. the reciprocal of the length of the string. 

   The usual sonometer is horizontal, like the one below at Kenyon College, and the tension is supplied by the weight of the masses hung on the ends of the wires after they pass over the pulleys. This arrangement has the defect that the strings and bridge cannot be seen by the class. 

   The vertical sonometer at DePauw University is upright, and tipped back about 3° from the vertical. 
   The differential sonometer was invented by the French acoustical apparatus manufacturer, Marloye, ca. 1840. This has two strings, which may be used to illustrate beats if the two strings have almost the same frequency. If one string has twice the frequency of the other, octaves may be demonstrated. It is in the apparatus collection of Kenyon College in Gambier, Ohio.

   The Sonometer below was originally at Denison University. The apparatus collection catalogue at Denison notes that it was made by W. N. Clouse, and was in the lab in September 1885. It is now in the Greenslade collection.

REFERENCE: Thomas B. Greenslade, Jr., "A Vertical Sonometer", Phys. Teach., 24, 90-91 (1986)

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