.Calculating 'k' and 'w' in Wave Problem

[mikefitz]

http://img208.imageshack.us/img208/8093/untitledrp9.png

i understand how the 'k' and 'w' values were calculated in the above problem. what i do not understand is why 134 s and 20.9m are being take to the -1 power. is the 20.9m being added because the problem states the wave travels in the -x direction? Thanks

 

[OlderDan]

i understand how the 'k' and 'w' values were calculated in the above problem. what i do not understand is why 134 s and 20.9m are being take to the -1 power. is the 20.9m being added because the problem states the wave travels in the -x direction? Thanks

They are not. The -1 applies only to the units s and m respectively.

 

[billiards]

That -1 is a dimensional thing, it is related to the units. In fact I think it's a bit unusual to keep the units in midway through a calculation, it would have been better to bulk them together at the end, but don't let it confuse you!

Mathematically A^-x=1/A^x

It's just a notational thing, you'll note that it let's you do that rule where you can just add the powers when you're multiplying things together.

e.g. A²*A^-1=A²/A=A

so basically: m/s=ms^-1
and: 1/s=s^-1

 

[Hurkyl]

In fact I think it's a bit unusual to keep the units in midway through a calculation, it would have been better to bulk them together at the end, but don't let it confuse you!

Omitting units is a shortcut; if you want to write true statements, you have to carry the units throughout the equation. (And being careful with the units can prevent a good number of mistakes too)