Thanks for the replies.
Hi Alexfloo, in what way do you mean X can interchange? I do know that X are iid, but I don't see how this property can help when line 3 is adding more terms in reverse time order and line 4 is adding more terms in increasing time order.
Hi Chiro, I don't think it...
Suppose X is a random walk with probability
P(X_k=+1)=p and P(X_k=-1)=q=1-p
and S_n=X_1+X_2+...+X_n
Can anyone explain why does line 3 equal to line 4?
P(S_k-S_0≠0 ,S_k-S_1≠0 ,…,S_k-S_{k-1}≠0)
=P(X_k+X_{k-1}+⋯+X_1≠0 ,X_k+X_{k-1}+⋯+X_2≠0 ,…,X_k≠0)
=P( X_k≠0 ,X_k+X_{k-1}≠0...
I am currently solving a problem (similar to optimal control theory) involving optimization of an integral with mixed and pure constraints. eg: \int F(x,u,t) dt subject to x(t)\geq0 , u(t)\geq0.
The problem can be solved by Pontryagin minimum principle by introducing the Hamiltonian function...
v=Lf
L is wavelength and f is frequency.
I understand this equation but I confused the two.
In your example, if I increase f the speed will increase but it is not the case in a string.
I am not convinced that by doubling the frequency of the vibration the speed of the wave is still the same.
If the both equations are true for the string. The only way to have same tension and thus same speed but different frequency would be a different wavelength. But, that is from equation. How can I prove it or derive it? or maybe a more concrete example. Thanks.
Homework Statement
I do not understand the difference between v=f \lambda and v=\sqrt{T/\mu}
If a string is vibrated twice the frequency but the same tension as previous. Would the speed of the wave doubled?
I just plug in the value to get vx but my answer is different.
vx' is -0.8c in the answer booklet.
vx= -0.385c
But I thought that vx should have positive sign since the ball should move in the same direction from both frame S and S'.
I am trying to use relative velocity transformation to solve this problem.
By velocity transformation, from the reference frame S',
vx' = \frac{v_x-v}{1-\frac{v_xv}{c^2}}
where
vx'=velocity of the ball as observed by Ted = 0.8c
vx= velocity of the ball as observed by Jim
v = relative...
If I follow the same reasoning from my last post (photon takes time to travel from Ted to Mary), then time dilation will be observed. But if three of them are in the same frame, a photon still need to take some time to travel from Ted to Mary. So, time dilation should also be observed in this...
I think I get your idea of equal observed time. Length contraction works because Jim sees and takes two point in the space at the same time and measure their distance. So, no matter when Jim is doing the measurement, Jim will always get the same length.
I don't really get this part. One way I...
I don't really get what you mean. Maybe, I will try to explain my idea 1st.
Lets say both Mary and Jim start their clock immediately after Ted throws the ball.
When the ball reaches Mary (or Mary and the ball moving towards each other in Jim's frame), both of them stops their clock.
Lets...
http://i359.photobucket.com/albums/oo31/tanzl/JavaPrinting-4.jpg
Part c2 is wrong (where I need to calculate velocity)
Time dilation cannot be used here but I do not understand why.
Actually there are another part of the question before this
(b) According to Mary, how long does it take the ball to reach her?
I calculated the time in the reference frame of Mary.
Then, I convert it into Ted Frame using time dilation.
But, somehow it is incorrect.
There is a typo error in my...
Homework Statement
Ted and Mary are playing a game of catch in frame S', which is moving at 0.600c with respect to frame S, while Jim, at rest in frame S, watches the action. Ted throws the ball to Mary at 0.800c (according to Ted) and their separation (measured in S') is 1.8*1012m.
According...
Yea. Velocity transformation is another way of doing it. But the answer is different. Why I can't use time dilation to calculate the relative time taken for the ball to travel in this case?