If you decrease the distance between successive crests of a wave, this changes

Explanation:

Recall that

and

From Eqn(2), we can write

Using the identity , we can rewrite Eqn(1) as

Squaring the above equation, we get

Use Eqn(3) on Eqn(4) and we will get the following:

This simplifies to

Rearranging this further, we get

Putting to the left side, we get

Finally, taking the square root of the equation above, we get the expression for the muzzle velocity as