Question

The velocity V of sound waves through any materials depends on density p and modulus of electricity E. If V=KE^xP^y, where k is constant. Use the method of dimension to find the values of x,y, z and write the expression for V. Hence evaluate K.​

Answer 1

To determine the values of x and y using the method of dimensional analysis, we need to consider the dimensions of the given variables and their powers.Let's assign the following dimensions:Velocity V: [L][T]⁻¹ (length per unit time)Density p: [M][L]⁻³ (mass per unit length cubed)Modulus of elasticity E: [M][L]⁻¹[T]⁻² (mass per unit length per unit time squared)Using these dimensions, we can write the dimensional equation for V:

[L][T]⁻¹ = K [M][L]⁻¹[T]⁻²^x [M][L]⁻³^yComparing the dimensions on both sides of the equation, we can set up a system of equations:For the dimensions of length [L]:

1 = -x - 3y (equation 1)For the dimensions of time [T]:

-1 = -2x (equation 2)For the dimensions of mass [M]:

0 = y (equation 3)From equation 3, we find that y = 0.Substituting y = 0 into equations 1 and 2, we have:

1 = -x

-1 = -2xSolving the equations, we find x = -1 and y = 0.Therefore, the expression for V is:

V = K E⁻¹ P⁰

V = K/ETo determine the value of K, we need additional information or a specific example with known values of V, E, and P. Without that information, we cannot evaluate the constant K.Answer:

Step-by-step explanation: