How Do You Calculate Wavelength and Wave Speed?

[Sonny18n]

Homework Statement

1)The frequency of a wave is 4.0 x 10^7Hz. What is its wavelength?

Homework Equations

V= wavelength times frequency
f=1/T

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.

 

[berkeman]

Homework Statement

1)The frequency of a wave is 4.0 x 10^7Hz. What is its wavelength?

Homework Equations

V= wavelength times frequency
f=1/T

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.

What is the speed of light in m/s?

 

[Sonny18n]

What is the speed of light in m/s?

Straight from google;

299 792 458

 

[berkeman]

Straight from google;

299 792 458

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...

 

[Sonny18n]

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...

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

 

[berkeman]

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

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

 

[Sonny18n]

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

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

 

[berkeman]

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?

 

[Sonny18n]

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?

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

 

[berkeman]

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...

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

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

 

[Sonny18n]

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

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

 

[Sonny18n]

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

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

 

[berkeman]

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

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.

 

[Sonny18n]

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

 

[vela]

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?

 

[Sonny18n]

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?

I think so, but there's a lowercase "e" with a +21 at the end

 

[vela]

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?

 

[Sonny18n]

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?

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

 

[vela]

Try the calculation without using scientific notation.

 

[mfb]

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.

 

[berkeman]

@berkeman: We have MHz, not THz.

Oops, thanks mfb! Not sure how I misread the OP to get THz... LOL

 

[Meesh]

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

Sonny18n, Do you know why you are using the speed of light in this question?

 

[Meesh]

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

Okay, so you need to be sure to have your units straight here... These are the same *numbers* as what I calculated... But not the same amount of zeros. At all. I measured this in meters, what is the units for your number?

 

[Sonny18n]

Okay, so you need to be sure to have your units straight here... These are the same *numbers* as what I calculated... But not the same amount of zeros. At all. I measured this in meters, what is the units for your number?

Okay, revised answer, 7.0 x 10^14m

New question: a wave with a frequnecy of 31200 hz and travels at 790 m/s? What is the wavelenth in meters?

The first thing I did was divide 31200 by 790 but I somehow doubt that's right.

 

[Meesh]

Again, your equation is wavelength = speed / frequency. ( if you are unsure do a unit check... Does metres = [m/s]/(1/s) ? Yes. So you should just have 790/31200. Don't forget to look at the units to be sure... Or look at the equation. :)

 

[SteamKing]

Okay, revised answer, 7.0 x 10^14m

Nope, that's not it. 7.0×10¹⁴ m is about 100 times the distance from the sun to the outermost portion of the orbit of Pluto.

Look, the wavelength λ = c / f

You know c = 299 792 458 m/s and you were given f = 4.0×10⁷ Hz, where 1 Hz = 1 cycle / s

What's the wavelength?

 

[vela]

Okay, revised answer, 7.0 x 10^14 m

The speed, wavelength, and frequency of a wave are related by ##c = \lambda f##. According to the numbers you have, that would give you
$$3.0 \times 10^8\text{ m/s} = (7.0 \times 10^{14}\text{ m})(4.0 \times 10^7\text{ Hz}).$$ Just looking at the powers of 10, you should immediately recognize your answer can't possibly be correct.

Note that to enter ##3\times 10^8## on a calculator, you would enter 3, then hit the EE button, and then enter 8.

 

[Sonny18n]

The speed, wavelength, and frequency of a wave are related by ##c = \lambda f##. According to the numbers you have, that would give you
$$3.0 \times 10^8\text{ m/s} = (7.0 \times 10^{14}\text{ m})(4.0 \times 10^7\text{ Hz}).$$ Just looking at the powers of 10, you should immediately recognize your answer can't possibly be correct.

Note that to enter ##3\times 10^8## on a calculator, you would enter 3, then hit the EE button, and then enter 8.

Alright, so I did the EE stuff and got 7.5?

 

[vela]

So now you have ##3.0 \times 10^8\text{ m/s} = (7.5\text{ m})(4.0\times 10^7\text{ Hz})##, I assume. Does that seem reasonable?

 

[Sonny18n]

So now you have ##3.0 \times 10^8\text{ m/s} = (7.5\text{ m})(4.0\times 10^7\text{ Hz})##, I assume. Does that seem reasonable?

I certainly hope so.

 

[Sonny18n]

Again, your equation is wavelength = speed / frequency. ( if you are unsure do a unit check... Does metres = [m/s]/(1/s) ? Yes. So you should just have 790/31200. Don't forget to look at the units to be sure... Or look at the equation. :)

Okay, so is 2.53 cm an acceptable answer?

 

[Sonny18n]

Uh, I need help this oscillation question?

Water waves in a shallow dish are 6.0 cm long. At one point the water oscillates up and down at a rate of 4.8 oscillations per second.
a. What is the speed of the water waves?
b. What is the period of the water waves?

Oscillations? 6.0 cm is the wavelength probably.

 

[berkeman]

Uh, I need help this oscillation question?

Water waves in a shallow dish are 6.0 cm long. At one point the water oscillates up and down at a rate of 4.8 oscillations per second.
a. What is the speed of the water waves?
b. What is the period of the water waves?

Oscillations? 6.0 cm is the wavelength probably.

Please start a new thread with this new question. This thread is now locked.