What is the relationship between wavelength and frequency in a stationary wave?

[hotel]

Hi
what is the relation between wavelength (L) and frequency (f) ?
I know that

L = c/f

but if we have a stationary wave with no velocity (c), can we express wavelength with:

L = 1/f ?


thanks

 

[geosonel]

Hi
what is the relation between wavelength (L) and frequency (f) ?
I know that

L = c/f

but if we have a stationary wave with no velocity (c), can we express wavelength with:

L = 1/f ?

it is NOT correct that a stationary wave has no velocity. a stationary wave is caused by 2 waves traveling with the same velocity v in opposite directions. thus, for each separate wave:
(frequency f)*(wavelength L) = (velocity v)
the above equation IS the relationship between f and L

frequency has units (1/sec) and wavelength has units (meters). it is not correct that L = f^-1.

 

[hotel]

why frequency must be inverse function of time ? It can be inverse function of space as well I think, like f = 1/meter (number of cycles per meter)?!

If stationary waves have opposite velocities then practically they should cancel each other and the resultant velocity will be zero!

In my case, I have an steady state problem, where waves are function of space and not function of time. I don't think it make sense to use c when waves are not time dependent.

If L=1/f is not correct, how do we find the wavelength ?

( L=1/f seems to be the right answer, while I thought more about it since I posted the message)

 

[geosonel]

why frequency must be inverse function of time ? It can be inverse function of space as well I think, like f = 1/meter (number of cycles per meter)?!

If stationary waves have opposite velocities then practically they should cancel each other and the resultant velocity will be zero!

In my case, I have an steady state problem, where waves are function of space and not function of time. I don't think it make sense to use c when waves are not time dependent.

If L=1/f is not correct, how do we find the wavelength ?

( L=1/f seems to be the right answer, while I thought more about it since I posted the message)

so that we can better understand your comments, please post your actual problem and your work so far in solving it.

 

[Brad Barker]

the number of cycles per meter is the wavenumber divided by 2*pi.

:shy:

the reciprocal of frequency is period, which I'm sure you knew. and it should be clear that that period is not the same thing as wavelength.

also note that what's causing the standing wave is that there is something causing one end to vibrate, which sends a pulse through the medium (string) to the wall, the pulse reflects at this boundary with a 180-degree phase-shift, and this travels back to the original end. now, the wave is a standing wave because the frequency at which the free end is vibrating is such that it's sending out a pulse that happens to meet up with a reflected pulse at a certain point on the string.

(the easiest example is if they meet at the middle. then it's the entire length of the string that becomes a single wavelength of the standing wave.)

anyway, if you remove the source of vibration from the free end, you'd lose your standing wave!

despite the appearance of no motion, there actually is motion going on--you're just seeing the superposition (sum) of all the waves that are going back and forth along the string!

and you can find the speed of a single pulse traveling on that string that is creating that standing wave:

it's the frequency that the free end is vibrating with multiplied by the wavelength.


...i hope this helps you!

and now for a completely random smilie: :!)

 

[hotel]

thanks for your help

you are right, and I did a mistake about the wavelength.

So it seems that it is impossible to find wavelength from frequency, phase and amplitude without knowing some kind of velocity !

I hope this time I am on the write track !