Exploring Traveling Waves: Sin vs. Cos

[hotmail590]

For the traveling wave described by the formula

y(x,t) = Asin(kx-wt)


Then the wave is traveling in the +x direction. True or false?

In the physics textbook I have, it describes a traveling wave by y(x,t) = Acos(kx-wt), using COS instead of SIN. Is there a difference between these 2 formulas? If there is no difference then shouldn't the statement above be true?

Also

Would the wave Asin(kx+wt) travel in the opposite direction of Asin(kx-wt)?


Thank you for your help.

 

[lightgrav]

yes, whether you use sin or cos
is just a "phase offset" of 90 degrees,
essentially whether you want to watch
for cos: the peak of the wave
for sin: its upward-sweeping edge.

(kx-wt) contrast with (kx+wt)
for time just bigger than zero, where
is the argument still zero?
(x positive) contrast (x negative)
so the part of the wave you watch goes
(positive-x) contrast (neg-x) direction.

 

[hotmail590]

Thank you for your reply.

I would like to make sure if I have understood what you said.

So (kx-wt) moves in the + x direction and
(kx+wt) moves in the - x direction

The question I have says

Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time = 0
this new wave should have the same displacement as y(x,t) = Asin(kx-wt)

1 - Acos(kx-wt)
2 - Acos(kx+wt)
3 - Asin(kx-wt)
4 - Asin(kx+wt)

The correct choice would be 4 - Asin(kx+wt) right? Since it is asking for same displacement and amplitude at time = 0; therefore cannot be choice 2 - Acos(kx+wt).

Thank you for your help.

 

[lightgrav]

right - so if these two waves are on the same medium,
at t = 0 their displacements add everywhere,
with (4)+y(x,0) adding to 2Asin(kx)cos(wt) ...

answer (2)+y(x,0) adds to 2Asin(kx)cos(wt-45)
that is, their peaks won't line up, to add together,
until a little bit later time ... wt=45 degrees later.