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I have a question about wave speed..

I'm thinking about the concept of wave speed increasing while frequency remains the same.

I often see it represented like this for example when a wave goes from water to air.. so between two different mediums.. it goes faster through water, slower through air. The frequency remains the same. v=f*lambda, so the wavelength is higher in water.

And the wave front diagram they show makes sense to me

And a question can say.. this is the speed in water, this is the speed in air, this is the wavelength in water. What's the wavelength in air.

And I can work things out. I can calculate the frequency in water given the wavelength and speed in water. And then I have the frequency in air, and I also already have the speed in air, so I can calculate the wavelength in air.

But I am completely baffled how these things are transformed on a graph, or shown on a graph..

For example

Suppose a wave(call it wave A), is shown on a graph. And I now want to represent a wave(call it wave b), that is twice the speed of that wave, but the same frequency.

Here is why i'm baffled..

For wave B to be faster, and the same frequency, the wave length has to be longer, so wave B has to be stretched out relative to wave A.

But if I imagine wave B like wave A, and then stretch out wave B

So then I feel like now it looks like less cycles per second.. a lower frequency. Though it'd only be less cycles per second when stretched, if the x axis were time.

Though if the x axis were time, then if I stretched out the graph peak to peak, it wouldn't increase the wavelength.

So it seems to me that understanding velocity, time, wavelength and frequency on a graph is a complete different ball game depending on whether the x axis has time, or whether it has distance.

But I can't find any exercises that do that.. Where could I find such exercises?

Also, if you have a water wave, and it goes higher, from equilibrium to peak, so it has a higher amplitude, then it's clearly a longer wave, the wave is travelling more distance. Yet if a wave's amplitude increases, that isn't considered to be an increase in speed, because the only distance that counts in speed is wave length..

So isn't that speed ever taken into account.. And not just the speed that the wave takes to get from source to destination?
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4 months ago
#2
(Original post by gazbo1)
I have a question about wave speed..

I'm thinking about the concept of wave speed increasing while frequency remains the same.

I often see it represented like this for example when a wave goes from water to air.. so between two different mediums.. it goes faster through water, slower through air. The frequency remains the same. v=f*lambda, so the wavelength is higher in water.

And the wave front diagram they show makes sense to me

And a question can say.. this is the speed in water, this is the speed in air, this is the wavelength in water. What's the wavelength in air.

And I can work things out. I can calculate the frequency in water given the wavelength and speed in water. And then I have the frequency in air, and I also already have the speed in air, so I can calculate the wavelength in air.

But I am completely baffled how these things are transformed on a graph, or shown on a graph..

For example

Suppose a wave(call it wave A), is shown on a graph. And I now want to represent a wave(call it wave b), that is twice the speed of that wave, but the same frequency.

Here is why i'm baffled..

For wave B to be faster, and the same frequency, the wave length has to be longer, so wave B has to be stretched out relative to wave A.

But if I imagine wave B like wave A, and then stretch out wave B

So then I feel like now it looks like less cycles per second.. a lower frequency. Though it'd only be less cycles per second when stretched, if the x axis were time.

Though if the x axis were time, then if I stretched out the graph peak to peak, it wouldn't increase the wavelength.

So it seems to me that understanding velocity, time, wavelength and frequency on a graph is a complete different ball game depending on whether the x axis has time, or whether it has distance.

But I can't find any exercises that do that.. Where could I find such exercises?

Also, if you have a water wave, and it goes higher, from equilibrium to peak, so it has a higher amplitude, then it's clearly a longer wave, the wave is travelling more distance. Yet if a wave's amplitude increases, that isn't considered to be an increase in speed, because the only distance that counts in speed is wave length..

So isn't that speed ever taken into account.. And not just the speed that the wave takes to get from source to destination?
The issue is that in order to actually represent waves, you need to show change in both space and time. When you plot the amplitude of a wave on a graph with 2 axes, you have to either be showing how amplitude changes with time at a fixed point in space, or how it changes in space at a fixed point in time. These will often look pretty similar.
For your last point about amplitude with speed - amplitude has nothing to do with wavelength. Sure, if you plotted a sine wave and worked out the actual length of the curve (as opposed to the distance between two points of equal phase) then it's larger if the amplitude is greater, but this information isn't really useful on its own.
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