Question

Velocity of sound in air depends on pressure P, and density d.
Find the relation among them using dimensional analysis.​

Answer 1

Answer:

The velocity v of sound in a gas depends upon its pressure P and density ρ, shown by using dimensional analysis, show that ν∝

ρ

P

Medium

Answer

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V∝P

a

ρ

b

From the relation, using dimensional analysis,

Dimension of LHS= Dimension of RHS

∴LT

−1

=[ML

−1

T

−2

]

a

[ML

−3

]

b

⇒LT

−1

=M

a+b

L

−a−3b

T

−2a

Comparing LHS and RHS,

a+b=0

−a−3b=1

−2a=−1

On solving the equations,

a=

2

1

& b=

2

1

∴V∝P

2

1

ρ

−

2

1

⇒V∝

ρ

p

)(V−b)= constant. The unit of a is :

Medium

View solution

Hubble's law is expressed as (here, v= speed of recession, r= distance of galaxy, H= Hubble constant).

Explanation:

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