Check the correctness of relation v=√e/p , v= velocity of sound in a medium , p is density of medium and e is elasticity
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Answer:
We have to solve this problem using dimension.
The dimension of v is [v]=[LT
−1
]
Density d= mass/volume so [d]=[M]/[L
3
]=[ML
−3
]
Elasticity E= stress/strain, where strain is dimensionless
So dimesionally, E= stress = force/area or [E]=[MLT
−2
]/[L
2
]=[ML
−1
T
−2
]
Putting the dimension of each quantity in given equation,
[LT
−1
]=([ML
−3
]/[ML
−1
T
−2
])
x
=([L
−2
T
−2
])
x
By the principle of homogeneity of dimension, equating the power,
1=−2x or x=−1/2
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