Cardinal wave rules - accurate?

[azor ahai]

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1. wave velocity is determined by the medium
2. frequency never changes when a wave moves from medium to medium
3. wavelength does change when a wave moves from medium to medium

I had a hard time grasping how frequency is independent of wavelength. I have a tenuous understanding from looking at the units.

• Frequency is [cycles]/[T], wavelength is [L], and velocity is [L]/[T] - this gives us:
• [L]/[T] = [L][cycles]/[T] → [L]\[T] = [L]/[T] * [cycles] → 1 = [cycles] = constant.

So frequency is simply a measure of the number of cycles, which is a function of its energy while wavelength and velocity are derived from its energy.

1. Is this why frequency never changes when moving from medium to medium, but wavelength and velocity does?
2. Should I think of frequency as an inherent property of its energy?
3. Does frequency change in a dispersive medium?

 

[AwayFromReality]

Frequency is not necessarily independent of wavelength. When a wave changes the medium its traveling in, wavelength changes by some factor (lets says in this case its increasing). As a result, based on the equation speed = frequency * wavelength, speed would increase or frequency would decrease. If speed increases by the same factor as wavelength then frequency has to remain the same in order for the equation to still mathematically work. If frequency decreases by the same factor as wavelength then speed would have to stay the same. Physicist found that frequency stays the same so by the above equation when wavelength changes, the speed has to change.

 

[azor ahai]

Frequency is not necessarily independent of wavelength. When a wave changes the medium its traveling in, wavelength changes by some factor (lets says in this case its increasing). As a result, based on the equation speed = frequency * wavelength, speed would increase or frequency would decrease. If speed increases by the same factor as wavelength then frequency has to remain the same in order for the equation to still mathematically work. If frequency decreases by the same factor as wavelength then speed would have to stay the same. Physicist found that frequency stays the same so by the above equation when wavelength changes, the speed has to change.

I understand the v=fλ formula. But frequency is often in formulas lacking the velocity variable, while wavelength includes the velocity variable. Here are some examples:

• For light:
  
• for closed pipes:
  
• for open:
  

In the first example, frequency does't need a velocity term. In the second and third, it is the wavelength that doesn't need the velocity term.

Why?

 

[AwayFromReality]

Im not sure which three examples you're talking about since, at least on my end, I'm getting errors instead of the image

 

[erythrocyte666]

1. wave velocity is determined by the medium
2. frequency never changes when a wave moves from medium to medium
3. wavelength does change when a wave moves from medium to medium

I had a hard time grasping how frequency is independent of wavelength. I have a tenuous understanding from looking at the units.

• Frequency is [cycles]/[T], wavelength is [L], and velocity is [L]/[T] - this gives us:
• [L]/[T] = [L][cycles]/[T] → [L]\[T] = [L]/[T] * [cycles] → 1 = [cycles] = constant.

So frequency is simply a measure of the number of cycles, which is a function of its energy while wavelength and velocity are derived from its energy.

1. Is this why frequency never changes when moving from medium to medium, but wavelength and velocity does?
2. Should I think of frequency as an inherent property of its energy?
3. Does frequency change in a dispersive medium?

The first 3 statements are exactly true.
Frequency is independent of wavelength only when going from one medium to another (within same medium frequency and wavelength are interdependent)
This has to do with energy conservation as you say.
Each frequency would have a unique energy, at least for light. But as far as I know, mechanical wave energy is determined by a variety of additional factors (medium density, amplitude, velocity, etc.)
For question 3, look into phenomenon of chromatic dispersion. White light is made of all colors, each having different frequencies and hence energies; but if all light colors traveled at same speed, violet light would transmit more energy than red light in the path traveled. Hence, to keep rate of energy transmission constant, violet light must be slowed down, and this can occur if violet light is subjected to greater index of refraction. the higher the index, the more the light bends and hence you see rainbow. So frequency itself still doesn't change through the medium, but you will see dispersion to satisfy above condition.

 

[erythrocyte666]

I understand the v=fλ formula. But frequency is often in formulas lacking the velocity variable, while wavelength includes the velocity variable. Here are some examples:

• For light:
  
• for closed pipes:
  
• for open:
  

In the first example, frequency does't need a velocity term. In the second and third, it is the wavelength that doesn't need the velocity term.

Why?

It's not clear what you mean by frequency not needing a velocity term. You can always relate velocity, frequency, and wavelength to each other by v = fλ
L = nλ/2 and f = nv/2L are resonance requirements for the pipe closed on both ends; v = fλ still holds
For light, you can (probably) even combine the wave and particle natures of light E = hf and E = mc^2 to get f = mc^2/h to express frequency with a velocity term.