Simple Harmonic Motion Guitar String Question

[Apothem]

Homework Statement

Question: "The midpoint of a guitar string oscillates with an amplitude of 2.24mm with a frequency of 400Hz. Calculate:
i) The maximum speed at this point
ii) The maximum acceleration of the string at this point"

Homework Equations

Suitable formulas: x=Asin(2*pi*f*t) ; a=-(2*pi*f)²(x) ; v=(2*pi*f)(A)
where A= amplitude/m ; f=frequency/Hz ; t=time/s

The Attempt at a Solution

Attempted Solution:
I think I am alright with part i) I did: v=(2*pi*400)*(2.24x10^-3)=5.6ms^-1

However for part ii) I am a bit unsure, do I take x to be the amplitude, but at the midpoint would x not be 0, so the acceleration is 0 ms^-2?

(I originally posted this in the wrong section, and reposted it in the correct section, sorry if I should not have reposted it in a new section)

 

[olivermsun]

Your formulas under 2. are just for the displacement $x$ of a single point on the strong. There's no notion of the "midpoint" or any other point (think of the rest position of the point on the string as $y$).

 

[Apothem]

Your formulas under 2. are just for the displacement $x$ of a single point on the strong. There's no notion of the "midpoint" or any other point (think of the rest position of the point on the string as $y$).

Sorry, I am unsure on what you mean. I understand your first point, just not about the midpoint.

 

[olivermsun]

Question: "The midpoint of a guitar string oscillates with an amplitude of 2.24mm with a frequency of 400Hz. Calculate:
i) The maximum speed at this point
ii) The maximum acceleration of the string at this point"
...
However for part ii) I am a bit unsure, do I take x to be the amplitude, but at the midpoint would x not be 0, so the acceleration is 0 ms^-2?

Maybe I misunderstood what you posted earlier, but I think there is some confusion between the "midpoint" along the string (where x(t), v(t), and a(t) are given) and the "midpoint" of the oscillation (the rest position of the point, or where x=0).

 

[haruspex]

Maybe I misunderstood what you posted earlier, but I think there is some confusion between the "midpoint" along the string (where x(t), v(t), and a(t) are given) and the "midpoint" of the oscillation (the rest position of the point, or where x=0).

Yes, clearly the question means midpoint along the length of the string. It does look like Apothem has misinterpreted it as midpoint of oscillation.
Apothem, x is not the amplitude, it is the displacement at time t. The amplitude is the maximum displacement.