Standing and Traveling Waves

jcais

Is the period of a comination wave the same as the period of two traveling waves that make up this combination standing wave?

I googled it, but found nothing as of yet concerning equal periods.

Thank you for your time.

nrqed

The two traveling waves have the same angular frequency [itex] \omega [/itex], right? Now, what is the angular frequency of the resultant standing wave in terms of the angular frequency of the two standing waves? Is it twice the angular frequency of each traveling wave? I sit half of it? The same? One fourth?

If you are not sure, use algebra to prove it. Just add the waves
[tex] A sin( k x - \ometa t) [/tex]
and [tex] A sin (kx + \omega t) [/tex]

using the trig identity for sin(A) + sin(B) (the A here has nothing to do with the amplitude, it just represents and arbitrary angle).
What do you get?


Patrick

jcais

I am using an Excel document. It tells me to press F9 to make the waves move. The freq of the standing wave is easy to get. It is 3.15 seconds (the time it takes for an extreme to go back to an extreme). 1/3.15 = period. I am supposed to press F9 to move the traveling waves from one extreme to another. I don't know what an extreme would be. But, I did it and guessed that the freq. is also 3.15. The way I am describing this is confusing, because there is not much detail in words.

So, I guess the 2 traveling waves have the same freq. as one combo standing wave making them both have the same period because T = 1/f, if I am correct.

Thank you for your assistance.

nrqed

No, this is the *period*. The period is in seconds. And it is the time it takes for a point to go from an extreme position (say y=+A) down and back to its initial position.
that will be in Hz (Hz= 1/second) and that's the frequency.
You can check it with the trig identities for adding trig functions. But yes,, the frequency of the combined wave is the same as the frequency of the individual waves (if each wave has the same frequency)

Patrick