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# There is no real relationship between Speed and Wavelength in a medium?

Discussion in 'MCAT Study Question Q&A' started by ipodtouch, Mar 29, 2012.

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1. ### ipodtouchNew Member

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I am pretty perplexed by this question from BR Physics chapter 10, section 1

14.) What is true of different colors of light in a Medium?
C.) As speed decreases, the Wavelength decreases
D.) As frequency increases, the Wavelength decreases.

I am wondering why exactly choice D is favored over choice C. The BR says that "there is no distinct relationship between speed and wavelength." But then in the answer explanation for #18, "If the wave speed of the light is reduced, then the wavelength is also reduced.
2. ### pfactionEstablished Member

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I'm not sure about light, but what happens is normally when a wave enters a new medium, frequency doesn't change. If v=f(lamda), and frequency is 1 (same), v=lamda (proportional). Therefore, yep, if v decr so does wavelength.

Index of refraction = c/v, where v is less than C and thus N is larger than 1. Index of violet is greater than red, meaning it travels slower. It has a smaller wavelength than red, and TPR says that as frequency up (wavelength smaller), speed decreases.

D is implying that v=flamda, in a vacuum, I think.
3. ### SaintJudeNew Member

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Well, this was in relation to a different question but Kaplan actually touched upon this. Within a single medium, the speed is essentially the same from one light of frequency to another. They didn't say why, but I guess it's just a fact of life. Suffice it to say that between one visible light color to another (that's in a very small range) and even b/w UV light and visible light, the speed is relatively the same.

On the other hand the E = hc/ lambda = h (f) tells you that the energy per photon is higher for a higher frequency light. And that always applies.
Last edited: Mar 29, 2012
4. ### ipodtouchNew Member

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A heads up, the question does not involve any "change in medium"
It is referencing waves in general, traveling through just any one medium.
5. ### chiddlerEstablished Member

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exactly. and velocity of an EM wave doesn't change in a static medium.
6. ### pfactionEstablished Member

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Oh, if it's any wave, then the general v=fL will apply.
7. ### chaser0New Member

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I am not sure this is a valid reasoning in the context of this question. The question references "what is true of Different Colors" meaning it's referencing more than one EM wave. Wave 1-> has speed one, Wave 2-> has speed 2 and so on; and how do their wavelengths compare...

I believe that this is just a poorly designed question. Even the answer explanation states that Both C and D are correct. Just D is "more correct" than C...
8. ### ipodtouchNew Member

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I believe frequency of an EM wave doesn't change in a static medium too.
I think the question has to be referencing different waves.
9. ### ipodtouchNew Member

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Wow, things I learned in the past hour

1.) Frequency doesn't change when any wave changes mediums
-although wavelength and speed do

2.) All EM waves have the same speed in the same medium.

So when a set of EM waves phase from one medium to the other:
-both velocities shift to an identical value
-Frequency remains the same
enter---> smaller n value: increase velocity, all wavelengths increase
enter---> larger n value: decrease velocity, all wavelengths decrease
(magnitude of wavelength increase/decrease depends on magnitude of frequency)

as per
velocity
(c/n)=(frequency) x (lamda)
10. ### pfactionEstablished Member

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I'm taking an AAMC, so yeah. I'm currently doing Bio, put Physics on the side, but always good to balance more than one in the mind.

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12. ### chiddlerEstablished Member

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In a static medium, velocity of an EM wave does not change.

Therefore, C is impossible.

This question is testing exactly this logic.
13. ### hellocubedNew Member

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Whoa whoa whoa guys stop here, there is a lot of misinformation here. If anyone took more time to read through the answer explanation it would be clearer.

1.) The question is asking about different waves of different speeds. Not about a single EM wave changing speed. Hence C is very valid (BR states that it is indeed a true statement).

2.) All EM waves do not travel at the same speed in the same medium. Different waves of different frequencies travel at slightly different speeds in the same medium.
Illustration:
An EM wave travels from one medium to another of Higher n value.
Frequency does not change, so what happens? wavelength changes, and speed changes as well as a result.
Different EM waves of different frequencies have different speeds, in a single uniform medium.

3.) In the explanation, the only reason C is invalidated is because all EM waves are the same speed in a vacuum.
Hence C is not true in a vacuum. But D is true always for all mediums.

I suppose the lesson here given by BR is that a "vacuum" is considered to be a medium...?
14. ### ipodtouchNew Member

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Oh wow, thanks.

So different EM wave frequencies in a medium can have different speeds?

Learn one thing, then unlearn immediately.

Also, I didn't know vacuum was considered a medium.
15. ### pfactionEstablished Member

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#2 reminds me of a prism, which is where I got it from TPR. They're traveling at different speeds: red the fastest, violet the slowest, so violet refracts more.
16. ### 411309zzzzGold Donor

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Wouldn't red be the slowest because they have the largest wavelength therefore lowest frequency? Also e is equal to hf and if I recall dont higher energy waves typically travel faster?
17. ### circulus vitiosCпутник-1Gold Donor

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Chromatic aberration is an example of this. Two different frequency (color) lights travel at different velocities in a given medium (a lens.) The indices of refraction are different so the focus for each color light is different.
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/aber2.html

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I recall TPRH saying that wavelength and frequency has no effect on speed even though the equation shows a relationship (v=f*lambda). Princeton said velocity is merely a constant and independent of frequency and wavelength. Therefore, C is wrong. On the other hand, they said the frequency and wavelength are inversely proportional, so manipulating one will change the other and make D correct. The speed will change depending on medium according to the index of refraction equation (n=c/v) only. Based on this information I would have chosen D but I am still uncertain why frequency and wavelength doesn't have an effect on wave speed.

I have no idea why red light is faster than blue light in the same medium. But according to some sources, red light is faster than blue light in the same medium other than a vacuum (otherwise the same) due to v=c/n. I would suspect the shorter wavelength (blue light) with its higher energy and frequency to be faster, but I'm not strong enough in physics to determine this. But I guess that would be wrong if frequency is the same no mattter the medium. Therefore, wave speed is proportional to wavelength only. Longer wavelength = faster speed if frequency held constant.

I'm confused at this point. Please someone navigate me to the correct understanding.
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19. ### milski1K member

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Speed of light in a given media is a constant. It is almost but not exactly the same for all wavelengths.

For a lot of cases/experiments that difference can be ignored (for example - image created by a convex/concave lens) but it can be detected with certain experiments and it has to be considered sometimes (making a rainbow with a prism, for example). The slight difference in speeds in that media is known as "dispersion" in physics, "chromatic aberation" in optics. The reasons for it are well beyond what's tested on MCAT, is enough to know about it.

c=&#955;f is for a specific c. It tells you that you cannot vary &#955; and f independently from each other. If you want to take dispersion in account, for a given media you will have cr=&#955;r * fr and cb=&#955;b * fb - different speeds for red/blue and different wavelengths frequencies for each of them.

Frequency of an already emitted light stays constant as it transitions through different media. Since with each of these transitions c changes, the only possibility here is to change the wavelength when the media changes.
20. ### hellocubedNew Member

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It should be noted that the BR states specifically that C is true for all cases except the vacuum.

The "speed of light" is a generalization. But if frequency is held constant, then a change in wavelength has to result in a change in speed or else

c=f x lamda

is not true for all cases. Making D false as well.
21. ### milski1K member

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There is no practical way to do that. You cannot control frequency and wavelength independently of each other.
22. ### hellocubedNew Member

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I was considering the transition between mediums. (not as a situation, but as a "device" demonstrating a practical way of controlling frequency and wavelength independently)
f remains constant when transitioning between n1 and n2, but wavelength changes.

In effect, speed must change as well.

Or am I getting this the other way around?
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23. ### milski1K member

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That can work, by using different medias you can select different combinations of frequency and wavelength, although you will still have some limitations. It becomes a borderline philosophical argument at this point, but you're still not changing them independently, you're just changing the speed.

My point is that there are ways to create a wave with certain frequency and you can select speeds based on the media but for most waves you cannot change the wavelength (by moving the peaks, whatever) - you can only expect it to change as a result of different speed of propagation.
24. ### ipodtouchNew Member

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Wow, a lot of action here.

So in conclusion, the BR is correct?
Both C and D are valid, but because C is not valid in a vacuum, D is "more true" than C?
25. ### milski1K member

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I would say that if we keep it in MCAT's scope, C is not valid anywhere. It can be valid only if we consider dispersion but the reasons for it and how it relates to wavelength but these are not intro physics. Of course, that's just my opinion and I am neither TBR nor MCAT test writer.
26. ### ipodtouchNew Member

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Thanks

So wait. If there are two different EM waves created:
1.) lower wavelength
2.) higher wavelength
then 2 doesn't have a slightly higher speed than 1?
27. ### milski1K member

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They may travel at slightly different speeds. The effect is called dispersion. [End of MCAT material]. How big the difference is, including if 2 is faster or slower than 1, is a whole different story and is not covered in intro physics.
28. ### hellocubedNew Member

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Oh man let's put an end to this...

It would. 2 definitely would have a slightly higher speed than 1. In any medium always (except vacuums).

I believe milski is speaking in "practical experimentally impossible" terms. But then again the MCAT gives you a lot of hypothetical experimental situations.

If you come across a question like this, then you will have to follow
in the end.
29. ### milski1K member

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There is media for which 1 will travel faster. Which is why I would attribute any correlations between &#955;, f and c on the MCAT only to &#955;f=c and treat c as a constant in the media unless there is something explicit talking about dispersion.
30. ### hellocubedNew Member

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&#955;f=c is basically what I'm trying to convey.

If 2 wavelengths have the same frequency, but different wavelengths. And are in the same medium. According to the equation, they have to have different speeds.

regardless of dispersion or not.

I feel like I'm missing something here?
31. ### chaser0New Member

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I think Milsiki is saying that it is physically impossible for two waves to exist with same f and different wavelengths in the same media?
Could someone possibly clarify this.
32. ### ipodtouchNew Member

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Hi, could you illustrate a media where the opposite is true? I'm trying to go over the math in my head and have a difficult time picturing this.
33. ### milski1K member

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hellocubed, you're good, &#955;f=c is always correct. The problem is that the question asks for "a media" which to me means that c is constant and you cannot change it, thus C does not make much sense.

ipodtouch, sorry, I don't have an example (handy). What is the math that you're going over? You're looking for something like c=func(f) where f is the frequency. Keep in mind that c=&#955;f is not that - it applies for a specific, fixed c.

Or even better, something like cf=c * k(f) where k(f) is function of f, close to 1 which gives you how much different the speed is for that frequency.
34. ### hellocubedNew Member

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No, I don't think he's saying that. There is no such rule that illustrates this.
He's basically saying that you can't make 2 specific wavelengths so finely tuned to the parameters that we are setting. That is is experimentally impractical.

But the question is pointing out two wavelengths out of billions.
It's basically saying that:

Which relationship is true for basketball players?
A.) As height decreases, speed increases.

A is a true statement. Just because you cannot "shrink the size of an NBA player" doesn't make A an impossible choice.

I think it's just miscommunication on everyone's part.
Milski is just doing his best to help everyone.
35. ### milski1K member

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Please, don't argue about what I'm saying. The last two people who did it broke up - the ugly story is somewhere in the lounge.

Seriously though, what I'm saying is that in a given media, you cannot control frequency and wavelength independently of each other.
36. ### UrshumMurshumNew Member

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The speed of light doesn't change unless it goes through another medium.

The speed of light is constant. (In a constant medium)

Just like y =3x you wouldn't say 3 varies with increasing y or x. Treat the speed of light as a number [For purposes of this question]

However, it is true that the speed of light changes with a medium, but not with frequency or wavelength, so technically the speed of light isn't "just" a number.
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I'm glad to see us come together to help each other figure this thing out.

So...basically, you can't change c for a particular medium. So the issue with the colors is based on dispersion and deep logical thinking that goes into advance physics topics.

Therefore, in a vacuum the speed is the same for all waves (even red/blue) (3.x10^8 m/s). It only changes slightly in a medium other than vacuum, but theoretically, it shouldn't.

That's why I hate physics...so confusing. As long as I can answer questions using c=fl, and understand the concept, I should be good. Thanks everyone. Good job.
38. ### johnwanderingNew Member

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So question:

The speed of an EM wave ONLY changes when it is changing mediums?
And then, ALL EM waves have the SAME speed while traveling in a single medium?

Does this mean that the wave accelerates/decelerates in crossing the medium (causing speed disparities between different frequencies), and then accelerates/decelerates AGAIN in order to match an identical speed of light?

This definitely seems to be what you guys are talking about. That speed of light is only different in medium change, but is an absolute constant in the medium.
Also, I know that we always talk about "what's in the scope of the MCAT." If the MCAT asks if it is possible for different EM waves to have different speeds in a medium, then the answer would be False?