Lec 7 | MIT 8.03 Vibrations and Waves, Fall 2004

[stefanmorrow615]

This video went viral on South Carolina

[mdgreg]

Neat Stuff, Continuous Vs. Discrete.

[kazbak1]

Legend! =)

[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?

[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]

@hamsterpoop Cheers mate

[Gicior]

One thing really confuses me. Around about 47 or 48 minutes Prof. Lewin shows a "mountain" being sent along the string and a "valley" comming back. At the instant when there is a mountain, there must be more potential energy than when there is a valley, since the bits of mass of the string are at different heights, but the kinetic energy must be the same, since "v" squared is the same. Where does the extra energy go? Also from valley to mountain where does the extra energy come from?

[Gicior]

I think I figured it out. I guess the energy escapes upon reflection from the string via Nicole and into the Earth upon which she is standing, effectivelly making Nicole accelerate the Earth a little bit by pushing it with her feet, increasing its kinetic energy. When the string goes from valley to mountain it draws energy from the Earth by making Nicole accelerate the Earth by pulling it, decreasing its kinetic 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.

[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.

[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.