test the validity of formula v=√p/d dimensionally where P is the pressure d is the density of medium and v the velocity of sound
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Answer:
[v]=[LT
−1
]
η=
A
dx
dv
F
⇒[η]=
[L
2
][T
−1
]
[MLT
−2
]
=[M
1
L
−1
T
−1
]
[ρ]=[ML
−3
]
⇒[LT
−1
]=[M
1
L
−1
T
−1
]
x
[ML
−3
]
y
[L]
z
Equating the exponents of M, L and T on both LHS and RHS$$
⇒M
0
=M
(x+y)
⇒y=−x
For T,
−1=−x
x = 1
y=−x=−1
For L
1=−x−3y+z→−1+3+z
1=2+z→z=−1
⇒z=−1
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