2020 - 20
The speed of sound in air depends upon the elasticity coefficient of medium and density . establish formula for speed of sound by dimensional method?
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Explanation:
Elastic density of medium = d=mass/length=ML−3
Coefficient of elasticity E=stress/strain = ML−1T−2
let velocity v be = dn×Em
so L1T−1=M(n+m)×L(−3n−m)×T(−2m)
equating the powers of corresponding dimensions
n+m=0 so n=−m
3n+m=−1 => n=2−1 and m=21
So the formula is : v=KdE where K is a constant
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