Wavelength, frequency, and speed of a Standing wave.

[Jenn_Lane2001]

Hello,
Thank you all that helped me on the last problem. This other problem is also giving me a little problem.

Two sunusoidal waves travel in oppoiste directions interefere to produce a standing wave with the wave function.

y=(1.50 m) sin(.400x) cos(200t)

where x is in meters and t is in seconds. Determine the wavelength, frequency, and speed of the interfering waves.

Ok this is what I got...

Wavelength is =(velocity/frequency)
Frequnecy is = 1/time

now the problem i ran into is this is a simple plug in and find result problem however from the standing wave funtion what numbers go where. I can't seem to find it. Any help will be greatly appreciated.
Thank You

Jenn

 

[Mulder]

Standing waves are given by

Y = 2A*sin(kx)*sin(wt) if that helps?

edit; k = n*pi/ L too, where L is the fundamental wavelength, you should have enough now.

 

[Jenn_Lane2001]

ok so the wavefrequency is L = n*pi/k however what does n stand for and k. That is the problem I am having i am not sure what certian letters mean. Thank you for the help though.

 

[Mulder]

Ok a better one sorry is wavelength = 2*pi / k.

You probably know f = 2*pi / w, and c = f* wavelength.

Match that to the equation in my first reply and it should be straight forward.

K is the 'wavenumber' by the way. Try looking up standing waves in a textbook as well, it could help.

 

[Jenn_Lane2001]

ok I think i got it now

Frequency's , since it's the same as the standing wave's:
F = 200 / 2pi = 31.83Hz.

Wavelength's is, since the wavelength of the sinusoids is the
same as the wavelength of the standing sin(0.4x) wave. That's
2pi / 0.4 = 15.71meters.
Finally, the speed of the waves is just wavelength x frequency = 15.71m x 31.83/s = 500m/s.

Does this look right and did i do it right?