Calculating frequency in wavenumbers

[joho]

Calculate frequency in wavenumbers of laser of wavelength 514nm.

514nm = 19455 cm-1 or 1.9455 x 10E4 cm-1

2.998 x10E10 / 1.9455 x 10E4 cm-1 = 1.54 x 10E16

Q1. Is my answer correct?
Q2. What units is this in? Is it cm s-1?
Q3. What does this number actually mean?

[CraigD]

Originally Posted by joho

Calculate frequency in wavenumbers of laser of wavelength 514nm.
…
Q1. Is my answer (1.54*10^16) correct?

No.

Frequency and wavelength are defined in terms of one another and the speed of propagation of the wave by this fundamental formula:
Speed = Wavelength * Frequency

A useful mental image to remember this by is to think of a train with cars of a known length (say 15 meters). If we measure the rate, or frequency, with which these cars pass (say 2/second, or 2 hz), and multiply it by the cars’ length, we have calculated the trains speed (15 m * 2/s = 30 m/s).

In the case that led to joho’s questions, speed and wavelength are known, and frequency needs to be calculated.
Because we re told that light is being measured, speed is the speed of light, roughly 300000000 (3*10^8) m/s. The wavelength was given as 514 nm. “nm” is an abbreviation for “nanometer”, which is .000000001 (10^-9) m, so, in standard units, the wavelength is 5.14*10^-7 m

We can rearrange the fundamental formula to:
Frequency = Speed / Wavelength

and solve using the known speed and wavelength. In keeping with hypography homework tradition, we’ll leave the actual arithmetic as an exercise for joho, for him to post in this thread for checking when done.

Q2. What units is this in? Is it cm s-1?

No. “cm * s^-1”, more neatly written “cm/s” is a unit of distance/time, so is a unit of velocity.

Looking at the equation we wrote above, can see that Frequency must be a unit of speed / distance, which is a unit of (distance / time) / distance. So it’s a unit of “pure number” / time. In standard units, frequency is in units “counts per second”, which are known as Hertz, and abbreviated “hz”

Q3. What does this number actually mean?

An intuitive understanding of what the frequency of light or other particles really means is a slightly more advanced question than I think appropriate for this post. If we imagine light to be like water waves, of waves in a shaken jump-rope, though, what the frequency in hz actually measures is the number of high points (crests) in the rope you count going past you in 1 second. When you’ve done the calculation, you’ll see that for visible light frequencies, this is a much higher number than you could ever hope to count with your naked eye and any sort of manual counter.

[Titas Aduksus]

Originally Posted by joho

Calculate frequency in wavenumbers of laser of wavelength 514nm.

514nm = 19455 cm-1 or 1.9455 x 10E4 cm-1

2.998 x10E10 / 1.9455 x 10E4 cm-1 = 1.54 x 10E16

Q1. Is my answer correct?
Q2. What units is this in? Is it cm s-1?
Q3. What does this number actually mean?

Wavenumbers? We call them things Hz, (which is cycles or waves per second) - as previously stated f=cp/l where F = frequency (Hz), c=speed of light in free space (metres per second), p propogation constant (1 for free space around 0.70 for glass) and l (lambda) the wavelength in metres.

So fill in the numbers and wind the handle, as an exapmle a wavelength of 1 metre corresponds to a frequency of 300Mhz (in free space). If you have not been given a propogation constant just use 1.

Now you have had it explained two ways it should be a doddle.

One final thing 1nm is 1 billionth of a metre.

[joho]

Thank you for your help Craig and Titas. Very much appreciated!

3 x 10E8 / 5.14 x 10E-7 = 583.658 or 5.837 x 10E2.

PS I'm a she!

[CraigD]

Originally Posted by joho

3 x 10E8 / 5.14 x 10E-7 = 583.658 or 5.837 x 10E2.

The left side of the equation is correct, but you’ve made an error doing the division.

Dividing by 10E-n is the same as multiplying by 10En. So the correct answer (3/5.14) x 10E(8+7) = about .5836 x 10E15 = 5.835 x 10E14 Hz.

Using the standard prefix, this would be 583.5 THz, (pronounced “Tera-Hertz“).

Most scientific calculators could do the arithmetic for you, but it’s good to understand how to do it by hand.

[joho]

Thanks Craig, I was using the Exp button instead of the 10x button!