Question

I don't understand the mathematical representation of a traveling wave

Answer 1

if at t=o our wave has a displacement \[D(x) = Asin \frac{ 2\pi }{\lambda} x\]
and it travels a distance vt in time t
at t= t the displace is \[D(x) = Asin \left[ \frac{ 2\pi }{ \lambda } \left( x-vt \right)\right]\]

Answer 2

why is it x-vt if its traveling in the positive direction?

Answer 3

if the wave is travelling in the positive direction i.e right side , then u know the equation of the curve moving to the left with velocity v is y(x,t) = f(x-vt) . What dint ya get? :S

Answer 4

i was thinking that if our displacement is increasing should it be x+vt?
for example, if i was standing at x at t=0 then i walked a distance vt in the positive direction, my new position should be x+vt not x-vt?

Answer 5

the minus implies that the position is decreasing.. :(

Answer 6

actually its not like that, we gotta see the functions for e.g. lets take a function
y = x
this function has value 0 at x =0
and if we move the function 2 units to the positive x -axis i,e the Function has value equal to 0 when x is equal to 2 units , then new function becomes y = x-2 not y = x+2
(see if u put x=2 in the y =x+2 it becomes 4 and if u put x =2 in y = x-2 then it becomes 0) so if we move A units to the right the function become y = x - A , did ya get it yet?

Answer 7

oh ok, i see what you mean.. i had oversimplified the whole thing.. am not that good at maths but thank you very much!

Answer 8

yea u prolly need to learn the chapter FUNCTIONS .that will clear ur confusion :)

Answer 9

i don't have time but i understand now :)

Answer 10

see actually the example u gave is not a function x = x+vt u said, its not a function its an equation. Kinda confusing to clear it ! anyhoo, Good luck!

Answer 11

thank you! :D