# How to distinguish between actual speed of wave and transverse velocity given number of antinodes, amplitude, length, and frequency?

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?