There was a good question raised after class as to why there was a
minus sign on front of the bulk modulus (B) but not in front of the
Young's Modulus (Y). This has to do with the definition of which way
the pressure is defined. For Young's modulus, the Delta P term on top
refers to a stretching of the bar, so Delta L is positive (it gets
bigger), giving a positive Y (I kept talking about compressing the
bar, but I should have been talking about stretching it for
clarity). For Bulk Modulus, when a pressure Delta P is applied to the
liquid, it by definition pushes on it, thereby shrinking it and making
the volume smaller (Delta V is negative here). So in this case a minus
sign is placed in front of it to make B positive. The idea is that Y
and B are always positive so that when you take the square root, you
get a real value for the velocity.