(adsbygoogle = window.adsbygoogle || []).push({}); 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 0.381m. The maximum transverse acceleration of a point at the middle of the segment is 8200 m/s^2 and the max. transverse velocity is 4m/s.

What is the amplitude of the standing wave?

2. Relevant equations

[tex]y(x,t)=Asin(kx)sin(\omega t)[/tex]

3. The attempt at a solution

I figured that the wavelength in fundamental mode is given by [tex]\lambda = 2L = 0.762[/tex]. Then k is [tex]k=\frac{2\pi}{\lambda}[/tex].

The partial der. of the wave equation are:

[tex]\frac{\partial y}{\partial t}=\omega Asin(kx)cos(\omega t) = 4[/tex]

[tex]\frac{\partial^2 y}{\partial t^2}=- \omega^2 Asin(kx)sin(\omega t) = 8200[/tex]

I'm not sure what to do next. The time variable in the equation is confusing me, there are 3 unknowns (omega, t, A) but I only have these two equations.

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# Homework Help: Standing wave Amplitude

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