Questions concerning the Theory of Relativity, sound, and light.

[Haibane]

Hello again. Been working on the online homework and I'm somewhat stuck with one of the problems. With the other one, I would just like to confirm I have the correct idea in mind.

Thanks!

First the question which I am having the problem with.
1) In which of the following statements about sound waves is NOT true about light waves?

a) Two sources of sound can sometimes interfere with each other so no sound is heard.
b) Sound waves of different frequencies sometimes travel at different speeds, depending on the medium
c) The Doppler effect depends on the motion of the source and receiver with respect to the motion of the medium of the sound.
d) A special type of sound wave (a sonic boom) is associated with objects which move faster than the speed of sound in the local medium


I believe A is not the answer because as far as sound goes, sound waves iirc can cancel each others waves do not synch. And light can also cancel out (as seen by the dark slits in Youngs slits experiments"

I believe B is not the answer because both light and sound are distorted when moving through other mediums. This can be seen with something like water. Which distorts both sound, and also distorts light by distorting the appearance of objects that are looked at from over the water.

I believe the answer may be C, but I am not quite sure why.

But I believe it may have to do with the fact that the movement of light
does not change depending on the objects which are observing the speed
of light while moving or stationary.

D) Would also not be the answer, since iirc the professor had also mentioned that light does sometimes create an effect when it moves past the speed of sound which can be observed under some circumstances.



Now the two I believe I am correct about, but just want verification.
_____
2: If you travel at near the speed of light to the star Alpha Centauri 4 light years away and then return to Earth about a decade will have passed on Earth. Yet you will have aged less than a year (depending on exactly how fast you travelled). To people on the Earth the reason is that time ran more slowly aboard your moving spaceship than it did on Earth. What is your explanation for the fact that you aged so little?

a)You noticed yourself that your clocks were running more slowly than usual
b)As you were traveling you measured the distance to Alpha Centauri as actually much less than 4 light years
c)You actually went backwards in time while turning your ship around
d)This is wrong, there is no way to return from Alpha Centauri in less than 8 years, because you cannot travel faster than light

I believe the answer is B.

This would be related to time dilation. Which an also be explained by the equation: Change in time = Light years traveled/ square root of 1 - v^2/c^2

____
3: The formula E=mc2 says that Energy = mass times the speed of light squared. What does this formula mean in the case of a beam of light with Energy E?

a)That when the light ray is absorbed by matter the mass of the absorbing matter will increase by E/(c*c)
b)That the light ray is affected by gravity as if it itself has mass equal to E/(c*c), even though it is not a material substance
c)That the matter which emitted this light ray now has less mass by an amount E/(c*c)
d)All of the above

I believe it is D for the following reasons. Considering that mass is considered a form of energy. This means that energy would also have some "weight" to it. This means it would a) cause the object absorbing that light ray to gain the mass of that light ray. b) The energy having mass would be affected by gravity. This can also be seen by the fact that even light cannot escape some gravity fields (ie black holes). C) conservation of energy would dictate that it cannot be created or destroyed. So the light that left the object would take it's mass with it when it left. Thus making the item which it left lighter.




Hope you can make sense of this. I've been going at these problems for a while. And in reading the text, my brain is somewhat scrambled in trying to get my mind about the whole concept of relativity >.<

If you can't please let me know and I will reword or rewrite this!

Thanks again!
-Haibane

 

[Mindscrape]

For the first one I would believe it is D because, as far as I am aware at least, there is nothing like a sonic boom for light traveling faster than the speed of light. While it is possible to exceed the speed of light in certain mediums, I don't think there is anything synonymous to the boom. (I am fairly certain C is right because it looks like it has just phrased the doppler effect into words.)

The second one would be right, because once you start traveling faster the distance measured in the frame will be smaller. However, there would actually be a contradiction (refered to as the twin paradox) that in your reference frame it is the Earth that moves faster and has its clocks slow down. So you would think everyone on Earth would be younger, while they would think you were older. This can be reconciled by the fact that you had to have accelerated, and left an inertial reference frame, to get to the speed of light.

This is only part of the equation I know for energy, which comes about only for an object at rest. The equation I know is that E^2 = (mc^2)^2 + (pc)^2. But your reasoning for D seems good.

 

[robb_]

There is such a "sonic boom" for light. It is called Cerenkov radiation and is really cool. Check it out!

 

[denverdoc]

for first one, I believe it is c. Altho its confusingly worded, I believe it is asking about whether there is a preferential direction of movement. In other words, light speed is not dependent on the movement thru a medium--this was the basis of the Michaelson-Morley experiment iirc-if there was an ether thru which the Earth moved, there should be differential rates of speed of light which could be measured by such an experiment. speed of sound is definitely different going upwind versus down.