Sound waves and EM waves - frequency/wavelength confusion!

[The_Sunny_Doc]

Why is it that wavelength and frequency are related with EM waves, but with sound, the point of emphasis is that its only dependent on stiffness/tension and "heaviness" (density) of the medium? Why do they talk more about the frequency/wavelength inverse relationship with EM waves? I'm just kind of fuzzy on this point.

I know the frequency of a wave only depends on the source, but that frequency and wavelength are inversely proportional, and that wavelength gets longer/shorter when light refracts through media (water, air, etc) and a prism... basically, lots of theory floating in my mind. Can someone clear it up? Just trying to nail down the frequency/wavelength thing for both EM radiation and sound.

Thank you in advance. I'll mail you home baked cookies if you can help me out, lol.

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[Synapsis]

The frequency/wavelength relationship exists for all waves that we're concerned about for the MCAT. The speed of a given wave depends on it's type (EM or sound for MCAT) and the medium through which it propogates. There are equations that tell you something about how fast a sound/EM wave will go in a medium of a certain "stiffness" or density. They act oppositely.

EM waves tend to move slower in more optically dense mediums (higher n value). This is shown by the equation v = c/n where v is the speed of the EM light in a given medium with a certain n value. Sound waves tend to move faster in denser mediums. This is shown by the equation v = sqrt( T / u ). T is the "restoring force" or tension, and u is basically just the inertia. This is why sound moves faster in solids. Solids have a large restoring force. This should also make sense conceptually. Sound waves move based on how fast molecules vibrate right? High restoring force means they vibrate really fast. This equation also explains why, if you have a gas sample of hydrogen and a gas sample of oxygen, sound moves more slowly in the oxygen sample. That sample has more inertia (but both are gases and have similar enough restoring forces).

So you're right, frequency depends on the source. But Doppler Shifts can give a perceived frequency different than that of the source. This occurs when either or both of the emitter and listener are moving toward/away from each other. All waves (for the MCAT, including EM waves) can undergo Doppler Shifts. So if I'm screaming because I'm stressed for the MCAT and I'm running toward you, the frequency of the sound waves is larger, right? What about the speed? It's the same as if I was standing still because remember the speed is dependent on the type of wave (sound in this case) and the medium, and the medium is the same whether I'm running or standing still. But notice since the speed v is the same but the frequency f has increased, you can use the relationship v =fw (w is wavelength) to see that the wavelength has to be shorter. So you can still use this relationship for sound waves.

For refraction, the way I remember it is just knowing that there's an inverse relationship between wavelength and the amount of refraction. Bigger wavelength (red, in the visible spectrum), less refraction.

I expect those cookies in 36 hours.

 

[The_Sunny_Doc]

Thank you. That was very helpful! Totally crystal clear. You rock, Physics mastah!

One point that I wanted to clear up, jumping off what you said, was that longer wavelengths refract the least but diffract the most, right? That confused the heck out of me looking at those diffraction gratings with red and violet stripes after looking at prism problems. The red stripes are at the outer edges of the bands produced by diffraction gratings. However, red is bent the LEAST amount (=deviates least from original light path) when you look at prisms. I don't know the underlying reasoning but I think that's how it goes.

If you're serious about cookies, pm me your mailing address, and I'll have them out after the test Friday, hehe.