Changing media: frequency stays constant, wavelength changes. Why?

[Kangaroo Paw]

Hey guys!

Just a quick physics question related to sound waves: when a sound wave travels from one medium to the next, why is it that the frequency stays constant, but the wavelength changes? Is this because the frequency is only dependent on the source? I, for some reason, can never really distinguish frequency and wavelength other than the fact that they're inversely related...

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[geeyouknit]

Hey guys!

Just a quick physics question related to sound waves: when a sound wave travels from one medium to the next, why is it that the frequency stays constant, but the wavelength changes? Is this because the frequency is only dependent on the source? I, for some reason, can never really distinguish frequency and wavelength other than the fact that they're inversely related...

I think you're right. It's only dependent on the source, in that the frequency, f, is determined by the energy emitted. Energy = plancks* frequency, E = hf. If an electron drops to some level and releases X joules, that corresponds to X/h frequency, which won't change based on the medium. But wavelength changes because the velocity changes when going between mediums, and since V= w*f, if frequency is constant, and V decreases, w must decreases as well.

I think that's true for all waves, not just sound waves.

 

[mitchlucker]

If it applies to all waves then why does the refraction of light occur?

Ie- if white light is emitted at E=hf, then it passes through a prism, the light is split up into colors of different wave length. However, the speed of light is the same, so the frequency has to be different?


Nevermind, just looked it up. It's only from a 'monochrome' source that this is true, which are said to be impossible.

I'm assuming that sound is said to be a "monochrome" source for the MCAT and light is not.

 

[geeyouknit]

If it applies to all waves then why does the refraction of light occur?

Ie- if white light is emitted at E=hf, then it passes through a prism, the light is split up into colors of different wave length. However, the speed of light is the same, so the frequency has to be different?

Not sure what you mean by the first part? But I don't think frequency changes, it's the velocity that changes and has to, via the equation, change the wavelength.

I don't think white light is emitted in that sense. White light is the combination of colors of all the frequencies of the the visible spectrum, but each color is separately emitted.

I think the prism thing is something different called chromatic dispersion. From what the EK book says, the index of refraction of a medium can vary slightly with the frequency that enters. Something with a lower frequency (higher wavelength, ie , red light) has a slightly lower index, so it won't slow down as much as something with a higher frequency (violet light), so lights of different colors and different frequencies do exit the prism at different velocities so we can see the diff colors.
So the prism actually separates via frequency (which I guess is the basis of color).

But that's what I understand from only EK, which I trust. I haven't taken a class on it, so someone more educated should let us know.

 

[Kangaroo Paw]

I think you're right. It's only dependent on the source, in that the frequency, f, is determined by the energy emitted. Energy = plancks* frequency, E = hf. If an electron drops to some level and releases X joules, that corresponds to X/h frequency, which won't change based on the medium. But wavelength changes because the velocity changes when going between mediums, and since V= w*f, if frequency is constant, and V decreases, w must decreases as well.

I think that's true for all waves, not just sound waves.

Ahhh, thank you! That was very helpful, that makes a lot of sense. Thank you!

I guess I'll append another question to this one: I'm really not understanding the whole veolocity changing when changing media thing. The EK book talks about different materials in terms of elasticity (the greater the elasticity, the greater the velocity of the wave because the material "snaps back" with more ease, which lets the wave propagate with more facility), and in terms of "inertia" (not really sure about this to be honest... the material's resistance to motion? How heavy the material is to actually move?). However, after completing the questions, it seems as if the book contradicts itself a bit, or maybe the topic is just kind of vague. I don't understand why waves propagate faster through solids than through gases. I'd think that solids were more dense, leading to the wave propagating more slowly. However, the book claims that since solids are not compressible, there is less resistance to motion when the waves propagate.

Sorry for the long schpiel: could someone clarify the velocity issue? I'm afraid a bit confused. Geeyouknit, your explanation was awesome!!

 

[circulus vitios]

Ahhh, thank you! That was very helpful, that makes a lot of sense. Thank you!

I guess I'll append another question to this one: I'm really not understanding the whole veolocity changing when changing media thing. The EK book talks about different materials in terms of elasticity (the greater the elasticity, the greater the velocity of the wave because the material "snaps back" with more ease, which lets the wave propagate with more facility), and in terms of "inertia" (not really sure about this to be honest... the material's resistance to motion? How heavy the material is to actually move?). However, after completing the questions, it seems as if the book contradicts itself a bit, or maybe the topic is just kind of vague. I don't understand why waves propagate faster through solids than through gases. I'd think that solids were more dense, leading to the wave propagating more slowly. However, the book claims that since solids are not compressible, there is less resistance to motion when the waves propagate.

Sorry for the long schpiel: could someone clarify the velocity issue? I'm afraid a bit confused. Geeyouknit, your explanation was awesome!!

Look at the first formula: http://en.wikipedia.org/wiki/Speed_of_sound#Basic_formula "Thus the speed of sound increases with the stiffness (the resistance of an elastic body to deformation by an applied force) of the material, and decreases with the density."