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The speed v of sound waves in air depends on the atmospheric pressure P and density r of the air. By using the method of dimensional analysis, find an expression for v in terms of P and p.

The speed v of sound waves in air depends on the atmospheric pressure P and density r of the air. By using the method of dimensional analysis, find an expression for v in terms of P and p.

Grade:12th pass

2 Answers

Arun
25750 Points
4 years ago
The speed  of sound in air depends upon the pressure  and density of air .
Therefore,
.
Let, 
Dimensions of velocity, .
Dimensions of pressure, .
Dimensions of density, .
Comparing the dimensions of both sides of relation (1), we get,
which gives,
Using these values,
where,  is the constant of proportionality.
 
Vikas TU
14149 Points
4 years ago

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