Atmospheric Physics: Brunt Vaisala frequency question

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Homework Statement

Gravity Waves. Consider a pattern of motion in which fluid elements move at an angle θ to the vertical. Show that for an atmosphere where the Brunt-Vaisala frequency is ω_B the elements will oscillate with a frequency ν = N cos θ.

Homework Equations

, -Brunt Vaisala frequency,
g= gravity
θ = potential temperature


v= N cos θ -desired frequency of oscillation of the elements.

N= Brunt Vaisala frequency
θ = angle in rads (I know it's confusing here but wikipedia linked theta for potential temperature and I don't know how to make equations yet).

The Attempt at a Solution

Is ω_B supposed to be something?

So I know that the Brunt-Vaisala frequency is the buoyancy frequency, is it just a frequency with respect to the vertical?

In which case the answer is just to multiply N by cosθ? This could be it, but the part where they define N=ω_B confuses me, though there is more to the question.