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*Question:* The speed of sound in a gas might plausibly depend on
the pressure , the density , and the volume of the gas. Use
dimensional analysis to determine the exponents , , and in the
formula

where is a dimensionless constant. Incidentally, the mks units
of pressure are kilograms per meter per second squared.

*Answer:* Equating the dimensions of both sides of the above equation, we
obtain

A comparison of the exponents of , , and on either side of the
above expression yields

The third equation immediately gives ; the second equation then yields ; finally,
the first equation gives . Hence,

** Next:** Motion in 1 dimension
** Up:** Introduction
** Previous:** Worked example 1.2: Tire
Richard Fitzpatrick
2006-02-02