Velocity of sound depends on density (p) and modulus of elasticity (E) (the dimensional formula of E is ML-1T-2) - Physics - Units And Measurements

Question

Velocity of sound depends on density (p)
and modulus of elasticity (E) (the
dimensional formula of E is ML-1T-2)
a) State the principle of homogeneity
b) Using the above principle, arrive at an
expression for the velocity of sound (Take
K=1)

Vaibhav T. · Accepted Answer

Dear Student,

The principle of homogeneity of dimensions states that an equation
is dimensionally correct if the dimensions of the various terms on
either side of the equation are same

velocity, v=kρxEywhere k is constantM0L1T-1=M1L-3T0xM1L-1T-2yM0L1T-1=MxL-3xT0MyL-yT-2yM0L1T-1=Mx+yL-3x-yT0-2ycompare the coefficientsx+y=0  
 1-3x-y=1    2-2y=-1  
 3y=12from 1x+12=0x=-12v=kρ-12E12v=kEρ

Velocity of sound depends on density (p) and modulus of elasticity (E). (the dimensional formula of E is ML-1T-2). a) State the principle of homogeneity b) Using the above principle, arrive at an expression for the velocity of sound. (Take K=1).

Velocity of sound depends on density (p)
and modulus of elasticity (E). (the
dimensional formula of E is ML-1T-2).
a) State the principle of homogeneity
b) Using the above principle, arrive at an
expression for the velocity of sound. (Take
K=1).