Lec 7 | MIT 8.03 Vibrations and Waves, Fall 2004

Many Coupled Oscillators - Wave Equation - Transverse Traveling Pulses and Waves

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Category:

Education

Tags:

• vibrations
• waves
• resonance
• superposition
• oscillations
• refraction
• reflection
• Snell
• Maxwell
• MIT
• OpenCourseWare
• Huygens

[elijahunderw25]

Your vid is a favorite on Mauritania

[stefanmorrow615]

This video went viral on South Carolina

[mdgreg]

Neat Stuff, Continuous Vs. Discrete.

[kazbak1]

Legend! =)

[hai2410]

@hamsterpoop Cheers mate

[hamsterpoop]

@hai2410

Taking the derivative of the left side with respect to "x" is the same as taking the derivative with respect to "theta" and multiplying it by the derivative of "theta" with respect to "x". This is simply the chain rule.

On the right, he's taking the derivative with respect to "x" as well. This makes it the second derivative.

Basically. He's taking the derivative of both sides with respect to "x".

[hai2410]

54:39

he's differentiating tan(theta) with respect to theta and delta y/ delta x with respect to x- not quite sure how this is valid, as he's not doing 'the same thing on both sides'- any help?

[hai2410]

Don't think about the effect of its weight, as thats a complication which isn't meant to be there for that example. However

yes there is potential energy in the stretching of the string as well as the velocity of it. at the parts where the displacement from the equilibrium is zero, it is the most stretched, and it is also moving the fastest- so you see energy is transported along the wave- the places with maximum displacement are areas of no energy and zero displacement have maximum energy.

[felipeben569]

Actually - I might be wrong, I'm not sure - if you do the derivation for the gravitational potencial energy that a point on the string has due to the wave, you'll see that it depends not really on height, but it depends on the displacement from the equilibruim position, like on a spring. So, both pulses - mountain and valley - have the same potential energy.

[gamesguru]

That's pretty deep man. I would just say that the rest of the string not in the valley (the majority) is displaced up just a bit. So although it is not displaced up as much, it has more mass. Either of us could be right.