Question

Q1.The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the expression for the speed of sound.

Answer 1

Answer:

v = C p^x \rho^y V^z,

where $C$ 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

{[L]}{[T]} = {[M]}{[T^2][L]}\right)^x\left(

{[M]}{[L^3]}\right)^y [L^3]^z.

A comparison of the exponents of $[L]$, $[M]$, and $[T]$ on either side of the above expression yields

1$  =$ -x -3 y+ 3z,  

0$  =$x + y,$  

-1$  =$ -2 x.$  

The third equation immediately gives $x=1/2$; the second equation then yields $y=-1/2$; finally, the first equation gives $z=0$. Hence,

v = C \sqrt{\frac{p}{\rho}}.

Explanation:

Answer 2

Answer:

donot know

Explanation:

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