# Wavelength with P/Q exponent equation-solve for P/Q

1. Jan 18, 2010

### afg_91320

1. The problem statement, all variables and given/known data
Speed of an ocean wave depends on the wavelength $$\lambda$$ in meters and
gravitational field. (see equation below). Find values of P and Q. K is a constant and has no dimensions

2. Relevant equations

V = K$$\lambda$$PgQ

3. The attempt at a solution

V=velocity, which is m/s
and i can disregard K because it is a constant which has no dimensions.
g = m/s2
$$\lambda$$ = m
plugging in the numbers; i get:

m/s = mP(m/s2)Q

here is where i get lost. i dont know how to bring the exponents down so i can solve for it

2. Jan 18, 2010

### Staff: Mentor

You have V = K LPgQ
(I used L in place of lambda.)
So LP = V/[K gQ]

To solve for P, take the log of both sides, then divide both sides by log L.

To solve for the other exponent Q, first solve for gQ in a way similar to how I solved for LP, then take the log of both sides, and divide both sides by log g.

3. Jan 18, 2010

### afg_91320

are you sure? i was workin on this with my prof and he told me not to take the log; thats what i thought of doing initially
and i have no numerical values for the equations; its all dimension analysis

4. Jan 18, 2010

### Staff: Mentor

OK, what's the exact statement of the problem? As you have it in post 1, it appears that you need to solve for P and Q.

5. Jan 18, 2010

### afg_91320

The speed of ocean waves depend on their wavelength $$\Lambda$$ (measured in meters) and the gravitational field strength g (measured in m/s^2) in this way:

v = $$\Lambda$$PgQ

where K is a dimensionless constant. Find the values of the exponents P and Q