Does the speed of a wave in a spring depend on the maximum speed of each coil?

[insertnamehere]

Hi again. I'm going crazy over this question. Does a longitudinal wave in a spring depend on the maximum speed of each coil? Me, I've always thought that the transverse velocity of the Particle or coil remains constant and independent of the wave speed itself. Am I wrong? Or did I misunderstand the question itself. I really need help. Thank you very much for your time.

 

[quantumdude]

Hi again. I'm going crazy over this question. Does a longitudinal wave in a spring depend on the maximum speed of each coil?

If that's the way the question appears in your book then it would make anyone crazy, because it makes no sense!

Does what about a longitudinal wave in a spring depend on the max speed of each coil?

 

[insertnamehere]

Here's the question: In a longitudinal wave in a spring, the coils move back and forth in the direction of wave motion. Does the speed of the wave depend on the maximum speed of each coil?
Maybe I don't understand the question, but I always though that the speed of each coil (which would be transverse due to the motion of particles perpendicular to the propagation of the wave) remains independent and has no effect on the longitudinal waves. But I'm sooo confused! Help!

 

[quantumdude]

Well, for a longitudinal wave traveling to the right the displacement $y(x,t)$ from its equilibrium position is $y(x,t)=y_m\sin(kx-\omega t)$. The wave speed is $v_{wave}=\frac{\omega}{k}$, and the maximum speed of a coil is $|(\frac{\partial y}{\partial t})_{max}|=|y_m|\omega$.

What does that tell you?