# Velocity and acceleration of a standing wave

1. Dec 4, 2011

### forestmine

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

A string with both ends held fixed is vibrating in its third harmonic. The waves have a speed of 192m/s and a frequency of 240 Hz. The amplitude of the standing wave at an antinode is .4cm. Calculate the maximum transverse velocity and the maximum transverse acceleration of the string at points along the string a distance of 40cm, 20cm, and 10cm from the left end of the string.

2. Relevant equations
v=-A*ω*sin(ωt)
a=-A*ω$^{2}$*cos(ωt)

3. The attempt at a solution

First thing I did was calculate the amplitude at each of those points along the string, using y=A*sin(ωt). I set 40cm=$\pi$, 20cm=$\pi$/2, and 10cm=$\pi$/4 given that when I solve for λ I get .8m.

I then solved for ω. ω=2$\pi$f gives me 1507.2 rad/s. Using that value for ω, and each of the amplitudes I found, I plugged them into the equations for v and a. At 40cm, I get a velocity and acceleration of 0, which makes sense. At 20cm, however, while my velocity is correct, but acceleration is incorrect. At 10cm, both my values for acceleration and velocity are incorrect. Not sure what step I'm missing here or why I can't seem to get the correct answers.

Any help would be greatly appreciated.
Thank you!

Last edited: Dec 4, 2011
2. Dec 4, 2011