Snells law

then why does the equation use the speed of light

The standard form doesn't. Could you please write out what you think is referred to as Snell's law?

Snell's law is typically this:

$n_1 \sin (\theta_1) = n_2 \sin (\theta_2)$

where n1, n2 are indexes of refraction. They can presumably be defined somehow for mechanical waves like water waves, because all waves refract and there's at least one proof that doesn't rely on the wave being light. In the case of light specifally, the index of refraction os easily understood as the ratio of the speed of light in that material to in vauum:

$n_1 = \dfrac{c_1}{c_0}$ where $c_0$ is the speed of light in vacuum.

this is the equatin that depends on light and so snells law does as it uses this term n1

That's only how the index is defined for light though. I am not aware of how you calculate the index for other waves, but they certainly refract anyway.

* Actually, just thought a bit more, and I'm pretty sure this is correct:

The version of Snell's law that all waves follow is something like this:

$\dfrac{v_1}{v_2} = \dfrac{\sin(\theta_2)}{\sin(\theta_1)}$

The only important fact is that the angle is related to the ratio of the old speed to the new speed. This is clearly defined for all waves. For light in particular, however, you can do a trick:

Cross-multiply:

$v_1 \sin(\theta_1) = v_2 \sin(\theta_2)$

Divide by some speed, say the speed of light:

[TeX} \dfrac{c_1}{c_0} \sin(\theta_1) = \dfrac{c_2}{c_0}\sin(\theta_2)

That's only how the index is defined for light though. I am not aware of how you calculate the index for other waves, but they certainly refract anyway.

* Actually, just thought a bit more, and I'm pretty sure this is correct:

The version of Snell's law that all waves follow is something like this:

$\dfrac{v_1}{v_2} = \dfrac{\sin(\theta_2)}{ \sin ( \theta _1)}$

The only important fact is that the angle is related to the ratio of the old speed to the new speed. This is clearly defined for all waves. For light in particular, however, you can do a trick:

Cross-multiply:

$v_1 \sin(\theta_1) = v_2 \sin( \theta _2)$

Divide by some speed, say the speed of light:

$\dfrac{c_1}{c_0} \sin(\theta_1) = \dfrac{c_2}{c_0}\sin(\theta_2)$

The ratios of the speeds in this expression are now properties of the material, because they talk about the speed in that material relative to some fixed constant. That's a good thing as it's a much easier operational definition that definining indexes using different refractions at different boundaries.

So if the wave was sound would the equation be the same but use 330m's instead of the speed of light?