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**A transverse wave on a cord is represented by D(x,t)=0.22 sin (5.6 x + 34 t)**

Determine the velocity of the wave and the minimum and maximum speeds of the particles in the cord.

Determine the velocity of the wave and the minimum and maximum speeds of the particles in the cord.

So velocity can be found with v = f λ

f = ω / 2π and λ = 2π / k

so v = ω / k

= 34 / 5.6

= 6.1

I assume max and min speed of the particles means max and min of |D'| but how do I differentiate a time dependent function like this? I know the min will be at the amplitude and the max at the x intercept.

I've taken multivariable calculus but never had to apply it to a physical system so if someone could point me in the right direction I'd be grateful.