Q. velocity of sound in air depends on elastic constant
of the medium and its density. Using method of dimension
establish the formula for velocity of sound.
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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
Explanation:
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