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Grade: 12th pass

                        

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.

10 months ago

Answers : (2)

Arun
25768 Points
							
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.
 
10 months ago
Vikas TU
14149 Points
10 months ago
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