Question

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 formula​

Answer 1

Answer:

ANSWER

V∝Paρb

From the relation, using dimensional analysis,

Dimension of LHS= Dimension of RHS

∴LT−1=[ML−1T−2]a[ML−3]b⇒LT−1=Ma+bL−a−3bT−2a

Comparing LHS and RHS,

a+b=0

−a−3b=1

−2a=−1

On solving the equations, 

a=21 & b=21

∴V∝P21ρ−21

⇒V∝ρp