Good day! I'm having trouble comprehending this question.
Write the equation for a standing wave that has three antinodes of amplitude 2.00 cm on a 3.00 m long string that is fixed at both ends and vibrates 15.0 times a second. The time t = 0 is chosen to be an instant when the string is flat. If a wave pulse was propagated along this string, how fast would it travel?
The equation pertains to $y(x,t)=A_{SW}sin(kx)sin(\omega t)$, right? That's the equation for standing waves that is fixed at both ends.
Now, plugging everything in gives $y(x,t)=(0.04 m)sin[(100\pi rad/m)x]sin[(30\pi rad/s)t]$ I understand that, to get the transverse velocity, I need to get the partial derivative of the function in terms of $t$. The velocity is $\frac{6}{5}\pi m/s$.
However, when I read the question again, it seems that it asks for the speed of the wave since the frequency and length are given. Since the entire wave has three antinodes, the $\lambda $ should be $\frac{2}{3}L$, and I can use $v=f\lambda$ from there. My answer using this approach is 30 m/s.
Which is the correct approach?
