# wavelength

Discussion in 'Off-Topic' started by samjesse, Feb 19, 2010.

1. ### samjesse Thread Starter Active Member

Sep 14, 2008
202
0
Hi

Wavelength is defined as the distance in meter between the repeating points in a sine wave.
but the horizontal axis is in degrees and changing the scal can happen. then how in the world the units are in meters, it does not make sence to me. please help

thx

2. ### Mathematics! Senior Member

Jul 21, 2008
1,022
4
Well the formula for wavelength of an electromagnetic wave is
wf = c where w is wavelength , frequency is f , and c equals the speed of light

f is measured in hertz = s^-1
c is measured in meters per second or denoted m/s

Solving for w we have w = c/f
if you look at the units m/s / s^-1 = meters
the seconds cancle out.

the horizontial axis does have associate with it a time for each degree ,...etc

suppose you set t = 0 to corospond to degree 0 the time it takes for you to move thru a whole cycle of the wave would be the period.
Since d = rt we have the rate being the speed of light c and the time being the period again sense the speed of light is measured in m/s and period is measured in s we have that the horizontial distance is in meters
( this horizontial distance is what we call the wavelength of the sine wave..etc)

hope this helps
not much more to it.
Note c is the speed of light in a vaccum but the formula still holds more generally it is really just d = rt.

Another way to look at it is 360 degrees equals 2pi radians

if we are assuming a circle of radius 1 meter then the amount of radains for 360degrees would be the circumference of this circle which would be 2pi meters then every 360degrees on the horizontail would corospond to 2pi meter increments.
Ofcourse you would have to be sure that 2pi meters would corospond to 360 degrees in your application. so it is better to use the d = rt formula.

Last edited: Feb 19, 2010

Jul 7, 2009
1,585
141
Actually, you can look at things in a more general sense. A wave is anything periodic in some parameter (and it doesn't have to be a sine wave). Then the wavelength is the distance between two corresponding points on the wave. The parameter can be any physical unit or can even be dimensionless.

I'm finishing up a consulting contract where I've written a program that deals with digitized waves; since the abscissas are just the integers, there is no dimensional unit associated with the waves. These waves originally came from an oscilloscope, but the time information gets tossed away. Yet one can easily still measure the wavelength.

Of course, if you narrow the scope to typical moving waves in the physical world, you'll be talking about a real wavelength in length units, a frequency in time units, and a speed of propagation. You can relate angular measure to distance with a simple formula; see any basic physics textbook.

4. ### steveb Senior Member

Jul 3, 2008
2,433
469
Note that a sine wave in linear space (with distance indicated by $x$) can be written as follows.

$A=A_o\sin (\beta x + \phi)$

where $\beta={{2\pi}\over{\lambda}}$

Here $\phi$ is an arbitrary angular phase shift, $\beta$ can be thought of as a spatial frequency (i.e. radians per unit length) and $\lambda$ is the wavelength.

If you are familiar with time waves you can make a direct analogy as follows.

$A=A_o\sin (\omega t + \phi)$

where $\omega={{2\pi}\over{T}}$

Here $\phi$ is still an arbitrary phase shift, $\omega$ is the angular frequency (i.e. radians per unit time) and $T$ is the wave period (i.e. time for one cycle).

You may remember that the frequency (f, typically measured in Hz or cycles per second) is ${{1}/{T}}$. If so, then you can help your understanding by thinking of the number of cycles per meter as ${{1}/{\lambda}}$ in the case of spatial waves. In other words, ${{1}/{\lambda}}$ is analogous to $f$.

The above is a long-winded answer, but note that distance ($x$) and angle ($\theta$, measured in radians) are related in a clear way as follows.

$\theta={{2\pi}\over{\lambda}}x$

Your question can also be applied to time waves. In that case you could have asked how the time and the angle are scaled. Hopefully, you can now see the answer for both cases.