Why does frequency increase when wavelength decreases?

I need a proper explanation to why it happens, I just don't understand why.

Scroll to see replies

think of it this way, frequency means number of cycles in 1 second (say 10 cycles)
if frequency increases, that means 20 cycles in a second. comparing 10 and 20 cycles in a second, the wavelength in 20Hz should be smaller than that of 10Hz
hope this helps

Reply 2

Pangol

This is a very valid question, and I'd like to know the answer too!

To clarify what I think is being asked; if you have waves on string with a free end, for example, then the relationship between the frequency f of the waves, their wavelength w, and their speed v is of course v = fw. If f is increased, this equation tells us that several things could happen;

- the speed could stay the same, meaning that the wavelength would get shorter

- the wavelength could stay the same, meaning that the speed would get larger

- some more complicated combination, whereby both speed and wavelength alter

It's only the first that actually happens. Why? I've not been able to find an adequate explanation. I've seen explanations in specific cases (it's clear for light as it always travels at the same speed, there's an explanation for strings connceted with tension, etc.), but I've not seen an argument that deals with the general case. I wonder if it's a consequence of the conservation of energy.

Reply 3

Stonebridge

Original post by muh123

I need a proper explanation to why it happens, I just don't understand why.

Because they are related by

v = f \lambda

it means that in most cases, especially if the speed remains constant, if you increase f you decrease lambda.

It's worth noting that frequency does not always increase when wavelength decreases.
If you pass light through glass, its speed decreases and its frequency remains constant. This means the wavelength must decrease while the frequency stays the same.

With waves it tends to be frequency that is constant. You need to think more about how, in this case, wavelength varies with speed.

Reply 4

StephenP91

Doubt anyone knows "why". Though they can show you the formula and explain "why" that way, but that's not "why" at all.

Reply 5

Pangol

Of course, if there is refraction, then the speed and wavelength change while frequency is constant. But if we're just talking about waves in a single medium, no complications, and the frequency is increased, my understanding is that the speed stays constant and the wavelength correspondingly decreases. I'm not sure quite why!

Reply 6

shereez234

In terms of football:

Messi takes smaller length steps. Crouch takes larger length of steps.

so in 10 seconds messi can take 100 steps while crouch can take 50 or so.

so as step length of messi is smaller than crouch's messi's frequency is higher than crouch's frequency.

Reply 7

LethalBizzle

Firstly, the speed is constant (speed of light).

Now for an analogy. Imagine an infinitely long line of buses driving down an infinitely long road, with each one directly behind the other (no space, completely tailgating).

I stand at the side of the road and count the number of buses passing me. This is the frequency, f. The wavelength is the length of each bus. The speed of the buses is constant.

Naturally, if you have less long buses (shorter wavelength), the buses with pass me more often (higher frequency), and the converse is true also.

Reply 8

blue_shift86

simple! Think of it mathematically. Wavelength lambda = k/frequency. So as frequency increases, the wavelength gets smaller :smile:

. k is just a number of fixed value :P

Reply 9

gradu

Original post by shereez234

Reply 10

Pangol

Everyone seems to be finding different ways of explaining the wave equation. This isn't in question. We're all happy that v = fw.

The question is, for general waves, when frequency increases, why does speed stay constant? The wave equation would allow this, but also other alternatives.

(edited 12 years ago)

Reply 11

LeeC

Original post by Pangol

I guess it's to to with the conservation of energy, if the speed changed then this would require an acceleration which would need energy to be put in or taken out of the wave..but I don't know why this would rule out the other possibilities..

Reply 12

Stonebridge

Original post by Pangol

The question is, for general waves, when frequency increases, why does speed stay constant?

It doesn't.
Apart from light in a vacuum, the speed of a wave in a medium will vary with frequency or wavelength. It's called dispersion.

Apart from light in glass, which is well known, the speed of sound in gases in some cases will increase with frequency.
At higher frequencies in CO₂ for example.

The problem with the initial question is that it is asking why something happens which actually isn't universally true.
That's why the answer isn't straightforward and everyone is doing logical somersaults.

Reply 13

Pangol

Well that's a gap in my knowledge plugged. Thank you very much!

I was largely basing my ideas on questions such as 3(a)(iv) in this paper, which follows the principal I describe above. I presume that dispersion isn't something that can happen in this case. I still don't claim to see why it automatically follows that it is speed that stays constant and wavelength that changes rather than the other way around. (I know that this is easily verified experimentally, but that's not an explanation.)

Reply 14

Stonebridge

From the simple original question it's possible to get into quite an interesting debate.
The exam question you posted is clearly testing knowledge of the wave equation, and assumes that the speed of the wave does not change when the frequency is doubled.
This may or may not be true. But at A-level, students would assume that the speed of the wave doesn't vary with frequency. Indeed, you couldn't answer the question if it did as you would have no information on how it varied. Dispersion is only discussed in connection with light and the variation of refractive index with wavelength or frequency, I believe.

I'm not trying to nit-pick but am in danger of appearing to.

My point is that the original question is flawed, in the sense that it needs qualifying.

It would be similar to asking the question
"Why does the pressure of a gas increase when its temperature rises."
The problem is that you have to qualify this by adding "at constant volume". The pressure doesn't increase on heating if you allow the gas to expand appropriately.

Reply 15

Pangol

I agree with your nit-picking about the original question, which is why I tried to qualify it a little. It has been interesting to learn that, as with most things in reality, it's a bit more complicated than that!

When you say "at A-level, students would assume that the speed of the wave doesn't vary with frequency," why would they assume that (for waves other than light)? Experimental verification? Just because it is what they have been told? I'm still strugling to see a theoretical reason why is should be speed that stays constant rather than wavelength.

Reply 16

Pangol

And just to clarify a little...

If someone asked why refracted waves change their wavelength (and therefore speed) when they move between mediums, but not their frequency, a nice theoretical rationalisation would be that the waves are still being produced at the same frequency, so the same number of waves per second are arriving at the barrier between mediums, so the same number of waves per second pass into the second medium. You can't alter the number of waves passing a point in a second just because that point is in the second medium; they just keep coming. Therefore, frequency is constant, and it must be wavelength that changes, and speed changes accordingly.

That's the sort of explanation that I can't get a hold of in the situation we're talking about here.

Reply 17

muh123

The reason I'm asking is because my brain just crashed and burnt. I was investigating the frequency of a standing wave with wavelength. What I assumed was going to happen was as the length of the string increased the frequency would increase. However I found that the frequency decreased. What I pictured was If the length increased wouldn't it mean that more waves would have to be produced to form a Node as energy may be lost while travelling across a greater distance.

Reply 18

Pangol

Oh - that's an entirely different matter. We can't really answer that without more information. Are you talking about the fundamental frequency of the stationary wave? There must be more to the question than that.

Reply 19

Stonebridge

Original post by Pangol

At A-Level students would learn (but possibly not see proved) that the speed of a wave on a string is given by

v = \sqrt\frac{T}{m}

T is tension and m is mass per unit length.
It doesn't depend on the frequency (or wavelength) of the vibration.
In which case, the wave equation is all you need to know.
If you increase frequency you decrease wavelength, at the same wave velocity.

The speed of a mechanical wave in a medium depends on 2 things
an elasticity term (on the top)
an mass/inertia/density term (on the bottom)

The greater the restoring force in the medium, the greater the speed of the waves. This is because the wave motion is the result of the particles being displaced from their equilibrium position, and being returned to that by the restoring force. The faster they can return, the faster the wave can travel.
Of course, the mass of the particles has the opposite effect because the restoring force has to overcome this.