Question

the velocity of sound waves in a medium depends upon the coefficient of electricity of the medium E and it's density d. Establish the formula for the velocity of wave by dimensional method​

Answer 1

ANSWER

Elastic density of medium = d=mass/length=ML

−

3

Coefficient of elasticity E=stress/strain = ML

−1

T

−2

let velocity v be = d

n

×E

m

so L

1

T

−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=

2

1

So the formula is : v=K

d

E

where K is a constant

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