Solving Wavelength Frequency: 740nm Light

[konartist]

The speed of light is 3.0 x 10^8 m/s, given the equation c=(x)(v) where v has the unit of s^-1 what is the frequency (v) for the wavelength (x) of 740nm light?

For some reason I'm not getting the right units; maybe someone can find my mistake:

3.0 x 10^8 m/s = 740nm(v)

740nm x (1m / 10^9) = 7.4x10^-7 m

3.0 x 10^8m/s = 7.4 x 10^-7 m /7.4 x 10^-7

(3.0 x 10^8m/s) / (7.4 x 10^-7m) = V

I seem to be having a problem with my units. Can you have m/s/m ?
What exactly does it mean v has the unit of s^-1 ??

Anyone explain?

 

[neutrino]

740nm x (1m / 10^9) = 7.4x10^-7 m

No need to put nm there. You've already substituted the value for the 'nano' part.

3.0 x 10^8m/s = 7.4 x 10^-7 m /7.4 x 10^-7

??

(3.0 x 10^8m/s) / (7.4 x 10^-7m) = V

That seems to be right.

I seem to be having a problem with my units. Can you have m/s/m ?
What exactly does it mean v has the unit of s^-1 ??

In a sense, the m's cancel, which leaves you with 1/s.

v is the frequency of light. In simple terms, it tells you how many wave crests (or troughs) pass a point in a second. It's a number divided by time. Since numbers are not physical quantities with units, you are left with 1/s. There's a name for 1/s; it's know as Hertz, abbreviated Hz.

 

[Blueshift5]

Yes, it is possible to have m/s/m as a unit. In this case, it represents the speed of light, which is measured in meters per second, divided by the wavelength, which is also measured in meters. This results in a unit of 1/second, which is the same as s^-1. This unit represents frequency, which is the number of cycles or waves per second. So, in order to find the frequency (v) for a wavelength of 740nm light, we can use the equation c=(x)(v) and rearrange it to solve for v. This would give us:

v = c / x

Substituting in the values, we get:

v = (3.0 x 10^8 m/s) / (740nm x (1m / 10^9))

v = (3.0 x 10^8 m/s) / (7.4 x 10^-7 m)

v = 4.05 x 10^14 s^-1

Therefore, the frequency of 740nm light is 4.05 x 10^14 s^-1. This means that 740nm light has a frequency of 4.05 x 10^14 cycles or waves per second. I hope this helps clarify any confusion.