Speeds of particles of a wave on a cord

[endeavor]

Homework Statement

A transverse traveling wave on a cord is represented by D = 0.48 sin (5.6x + 84t) where D and x are in meters and t in seconds. Determine the maximum and minimum speeds of particles of the cord.

The Attempt at a Solution

I'm guessing these speeds are found by the partial time derivatives of D:
dD/dt = 40.32 cos (5.6x + 84t).

Is this right?
So the answer is 40.32 m/s??

 

[berkeman]

I believe that is correct. The partices on the cord only "travel" in a transverse fashion, so the time derivative is appropriate. You've correctly listed one of the maximum speeds (the other is just the negative speed). What is the minimum?

 

[endeavor]

I guess 0 m/s would be the minimum. But if you count -40.32 m/s, couldn't you say it is also the minimum (it's the smallest number). However, speed is technically always positive...but then why does it say "speeds"?

 

[berkeman]

I guess 0 m/s would be the minimum. But if you count -40.32 m/s, couldn't you say it is also the minimum (it's the smallest number). However, speed is technically always positive...but then why does it say "speeds"?

The problem should have been better stated, with "what is the maximum magnitude of the velocity...". Zero is the minimum speed, and +/-40.32 are the maximum speeds. You had the right intuition in solving this question. Unfortunately, some questions are not stated very well. The best response to badly stated questions, in my experience, is to gently point out the problem with the problem statement, state the best answers to the problem as stated, and gently offer the better-stated problem statement. Depends on the situation, of course.

Good work.