# Figuring out wavelength

1. Mar 15, 2015

### Sonny18n

1. The problem statement, all variables and given/known data
1)The frequency of a wave is 4.0 x 10^7Hz. What is its wavelength?

2. Relevant equations
V= wavelength times frequency
f=1/T

3. The attempt at a solution
1. Okay so I'm using the calculator on my iPod and I'm aware I'm supposed to use EE in some manner but don't know how.

Last edited by a moderator: Mar 15, 2015
2. Mar 15, 2015

### Staff: Mentor

What is the speed of light in m/s?

3. Mar 15, 2015

### Sonny18n

299 792 458

4. Mar 15, 2015

### Staff: Mentor

Put it into scientific notation so it is easier to do the calculation -- Use your equation "V= wavelength times frequency" and be sure to show units for each quantity...

5. Mar 15, 2015

### Sonny18n

That's the weird thing. It's shown as 3 straight numbers so are those spaces supposed to be commas? Like 200,000,000?

6. Mar 15, 2015

### Staff: Mentor

Roger that. So just re-write it as 2.99792448 * 10^__ [m/s] and set up your equation to solve...

7. Mar 15, 2015

### Sonny18n

Okay, that's 8 but where exactly is the speed of light supposed to fit into the equation?

8. Mar 15, 2015

### Staff: Mentor

Well, if it's a wave with a frequency in the THz range, that's pretty much guaranteed to be EM radiation. That would travel at the speed of light in a vacuum. Do you have any reason to believe it is traveling in a dielectric that would slow it down?

9. Mar 15, 2015

### Sonny18n

I'm not saying I don't believe you but it's weird that none of this is in the formulas given to me.

10. Mar 15, 2015

### Staff: Mentor

Yes it is. You listed it as a relevant equation already (see above quote). V [m/s] = Wavelength [m] * Frequency [1/s = Hz]...

11. Mar 15, 2015

### Sonny18n

Nowhere on my sheet does it mention a completely other number that is supposed to relate to the equation I'm solving.

12. Mar 15, 2015

### Sonny18n

Anyway, am I dividing speed of light by the frequency of the wave?

13. Mar 15, 2015

### Staff: Mentor

Yep, that's how you use that relevant equation. See how the units work out?

I have to bail for a couple hours. I'll check your answer when I get back.

14. Mar 15, 2015

### Sonny18n

Can anyone confirm if the answer is 749,481,120,000,000 ?

15. Mar 15, 2015

### vela

Staff Emeritus
As one of my colleagues would ask, "749,481,120,000,000 cows? Wow, that's a lot of cows."

The other comment I have is if you multiply that by the given frequency, would you get the speed of light?

16. Mar 15, 2015

### Sonny18n

I think so, but theres a lowercase "e" with a +21 at the end

17. Mar 15, 2015

### vela

Staff Emeritus
You might want to rethink that. The frequency is a pretty big number, and the wavelength you got is in the hundreds of trillions. Think about how big the product would be. Now while light travels fast, does it travel that fast? (The answer is no.) Can you come up with an estimate of how big the answer should be?

18. Mar 15, 2015

### Sonny18n

It is a ridiculously big number so should the 0's end at 120?

19. Mar 15, 2015

### vela

Staff Emeritus
Try the calculation without using scientific notation.

20. Mar 15, 2015

### Staff: Mentor

I guess the context makes it clear that we have an electromagnetic wave in vacuum? That should be given somewhere.

@berkeman: We have MHz, not THz.