Physics Wave properties.

Question

a)When a periodic wave excites a medium explain why the particles in the medium can have both velocity and acceleration? (4 marks)

 

 

b) What is the phase relationship between the velocity and the displacement? (2 marks)

 

c) Why is the velocity of the particles different from the velocity of the wave? (2marks)

 

Struggling with some theory. The penny isn't dropping, I hope this stuff isn't too complicated and someone can help.

Answer 1

Hi Ian!

 

(a) To be honest, I am not sure what they mean by "why" here, as if having velocity and acceleration at the same time is some rare occurrence.  They have velocity because some perturbing force did work on the medium that was transmitted to other parts of the medium through connecting forces between its particles.  They have acceleration for the same reason, as per Newton's 1st law of motion (a force accelerates objects).  Forces accelerate objects and thus change their velocity.   Is there something to this question that I am missing?  Please let me know.

 

(b)  In simple harmonic motion, in particular, the standard solution for the equation of motion for position as a function of time (as you may know) is:

 

x(t) = Asin(2πft) or Acos(2πft)  (you can choose based on, mainly, the initial conditions of the system)

 

where A is the ampltiude of the simple harmonic motion, and f is its frequency.

 

Either way, the expression for the velocity as a function of time for this system -- in calculus terms -- is the "first time derivative" of position.  This means that:

 

For x(t) = Asin(2πft) --> v(t) = (2πf)Acos(2πft)

For x(t) = Acos(2πft) --> v(t) = (2πf)A(-sin(2πft))

 

Since sine and cosine are functions that are basically 90^o or (π/2) rad out of phase with each other, this means that the position and velocity for simple harmonic motion share that 90^o phase relationship.

 

(c)  I am not sure what kind of answer they want here.  I would say that the oscillatory motion of the particles and the forward "motion" of the wave are related, but distinct, actions (much like the relationship between linear and angular motion for a rolling wheel).  Perhaps you could say that the velocity of the particles has to do with the force applied to them, and their mass (and thus acceleration), while the wave speed has to do with how quickly those forces are transferred to neighboring particles in the medium.

 

I hope this gets some things going for you!  If you would like to talk about it more, just let me know.