Solving for the Wave Equation y(x,t)

[dangish]

A scientist on a ship observes that a particular sequence of waves can be described by the
function y(x,t) =(0.800 m)⋅ sin[(0.628 m−1 )⋅ {x − (1.20 m/s)t}].
(a) At what speed do these waves travel?
(b) What is the wavelength?
(c) What is the period of these waves?

Can anyone tell me what form of a wave equation this is?

I think the key factor would be knowing that so I would find out what w(omega) is.

 

[Rick88]

http://en.wikipedia.org/wiki/Sine_wave

hope this helps!

R.

 

[dangish]

ok so..

i know that v= -wAsin(wt+phi) , phi seems to be 0 so i will ignore it in this case

however, comparing the link you gave me to that equation I have, it would appear that
w = -1.2m/s , but w is supposed to be in rad/s.

 

[Rick88]

Ok, forget phi.

Use this other general formula:
y(x,t) = Asin[kx - wt]

 

[dangish]

y(x,t) =(0.800 m)⋅ sin[(0.628 m−1 )⋅ {x − (1.20 m/s)t}]

comparing this to

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

would suggest

k=.628m^-1
w= -1.20m/s

which seems wrong to me because I know the units of w are rad/s

 

[Rick88]

how about expanding the bracket first?
0.8sin[0.628m-1 *x - 0.7536s-1 t]

 

[dangish]

that makes perfect sense,

now to get the speed i think I use,

v= -wAsin(wt+phi) ; phi = 0

which brings me to another problem, what is t?

could I simply use the period as t because I now know w.

I mean, w=2Pi/T ==> T=2Pi/w

then use T for t?

 

[dangish]

actually I don't think I can do that since part c.) asks for the period

 

[Rick88]

You had the velocity already.
From your initial form, you had (1.20m/s), which is indeed the velocity of the wave.

Afterwards you multiplied it by k to expand the brackets and obtain w, but kv=w!

 

[dangish]

haha, fair enough.

So, from the original equation, v=1.20m/s

part b.) wavelength = 2Pi/K ==> 2Pi/.628m^-1 = 10m ??

and part c.) w = 2PiT ==> T= 2Pi/w = 2Pi/.754 = 8.33 rad/s ??

 

[Rick88]

haha, fair enough.

So, from the original equation, v=1.20m/s

part b.) wavelength = 2Pi/K ==> 2Pi/.628m^-1 = 10m ??

and part c.) w = 2PiT ==> T= 2Pi/w = 2Pi/.754 = 8.33 rad/s ??

Yes, but careful with the units.
You're trying to find a time interval.

 

[dangish]

oh yes, units are seconds, silly me