The speed of sound in a gas depends on his pressure (P) and density (d) of that gas. Obtain the formula for speed of sound??
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11th
Physics
Units and Measurement
Dimensions and Dimensional Analysis
The velocity v of sound in ...
PHYSICS
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
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ANSWER
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=
21
& b=
2
1
∴V∝P
2
1
ρ
−
2
1
⇒V∝
ρ
p
HOPE ITS HELP YOU........
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