# Waves-displacement vs movement

How can a particle move downwards and be displaced upwards? Sounds paradoxical. I understand the part about movement but not displacement. What's the difference? Isnt displacement like the amplitude so when a particle in a transverse wave move down doesnt it mean its displaced downward?

## Answers and Replies

Simon Bridge
Science Advisor
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How can a particle move downwards and be displaced upwards?
The same way a skiier can be displaced a long way up a mountain but be moving (skiing) down it.
You have already met this sort of thing in your work on Newton's laws of motion.

I understand the part about movement but not displacement. What's the difference? Isn't displacement like the amplitude so when a particle in a transverse wave move down doesn't it mean its displaced downward?
When you displace a string in the +y direction, and let go, which direction does it move in? What physical quantity describes "movement"?

I'm sorry i still dont get the skiing part too :( hmm movement the physical qty is distance??

Simon Bridge
Science Advisor
Homework Helper
for movement, the physical quantity is "momentum" but I'd accept "velocity".
for position, the physical quantity is "distance", I'd accept "displacement".

something can have a positive displacement and a negative velocity if it is headed back to the origin.
have you not covered Newton's laws yet? kinematics? v-t graphs?

I have covered newton's law and i understand that part. I think i got you now :) so a particle will be displaced downwards irregardless of movement when it is below the eqm position?( in a graph of sinusoidal waves diagram)

Simon Bridge
Science Advisor
Homework Helper
That's right - in a wave of form ##y(x,t)=A\sin k(x-vt)## each point x will be oscilating about y=0 as ##y(t)=A\sin \omega t## the plot will give you a position-time graph. The velocity time graph is the derivative of this: ##v(t)=\omega A \cos \omega t## ... if you plot them above one another (so the time axis coincides) you'll see the relationship.

You should know from your Newton's laws and kinematics work that an object can be above the ground (positive height) and be falling (negative velocity). It's not just height that can be positive ... something with a negative horizontal displacement (say, it is to the left of the observer/origin and distances to the right are positive) can have a positive velocity (it is moving left-to-right). This should not be a mystery to you.