# Standing wave on a guitar string

1. Nov 11, 2007

### ronny45

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

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

3. 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.

2. Nov 11, 2007

### Vidatu

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

3. Nov 11, 2007

### 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?

4. Nov 11, 2007

### 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.