Question

The speed of sound v in gas might plausibly depend on the pressure p, and the volume V of the gas. Use dimensional analysis to determine the exponents, x,y and z in the Formula. Where C is a dimensionless constant. V=cp^xp^y V^z

Answer 1

Answer:

V= C√p/s

Explanation:

We are given that

Dimension of speed of sound

V = L T ^-1

Volume of gas = L³

Pressure P= M¹L^-1T^-2

Density =M¹L^-3

So

LT^-1 = C [M¹L^-1T^-2]^x [M¹L^-3]^y [L³]^z

Compare powers

We have

x+y=0

-x+3y+3z=1

-2x=-1

So x= 1/2 y= -1/2 z= 0

So finally we substitute in

V=cp^xp^y V^z

We have

V= C√p/s