Standing wave on a guitar string

[ronny45]

Homework Statement

A guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is 0.380m. The maximum transverse acceleration of a point at the middle of the segment is 8700m/s^2 and the maximum transverse velocity is 3.10m/s. What is the amplitude of this standing wave?

Homework Equations

y (x,t)= Asinkxsin$$\omega$$t

The Attempt at a Solution

$$\lambda$$ = 2L = 0.760m
k= 2$$\pi$$/$$\lambda$$=8.267
A= -$$\omega$$^2 y(x,t)=8700m/s^2
v y(x,t)=derivative of y(x,t) wrt t = 3.10 where y=0 (v max)
This is where I get stuck.

 

[Vidatu]

Remember, what is the highest value a sin function can have (ie what is the max of sin(anything) )?

 

[ronny45]

max of sin (anything) is 1. Em, I'm genuinely sorry if I'm being really obtuse here, but how does that help me?

 

[Vidatu]

No problem.

Also, I forgot to mention, keep in mind what is max of cos as well.

As you were given the max acceleration/velocity, it stands to reason that the sin values in your equation would be max, right? So, differentiate your displacement equation with respect to t, and pop in the trig values. This will give two much simpler equations, which you can use to solve for amplitude.