Solving Physics Questions: Muons, Speakers & Sound Intensity

[Pseudo Statistic]

Hi.
I'm having a bit of problems with this question:

A group of muons is observed to pass a balloon at a height of 480 meters above the Earth's surface. The muons move at a speed of 0.8c straight down towards the Earth's surface.
a) Calculate the time for the muons to travel from the balloon to the Earth's surface as determined by an observer on the Earth.
b) Calculate the time for the muons to travel from the balloon to the Earth's surface as determined by an observer moving with the muons. Explain your reasoning.

I have no clue how to do them because that "c" is throwing me off-- like, would they be moving with that constant velocity or will gravity be accelerating them further up to c and then they'll be moving with constant velocity, or is this some relativistic thing?

Also, let's say you had two speakers, a distance d apart and both a distance L away from an axis; i.e. something like this:
http://www.brokendream.net/xh4/physpic.JPG
Assume B, B and the speakers all lie on a vertical line and both speakers vibrate in phase and emit sound waves of equal amplitude and wavelength... and assuming d << L.
a) Describe how sound intensity I varies as a function of position x along the line segment OA. Sketch the graph of this function on an axes.

b) Assuming wavelength << d sketch a graph of the sound intensity I as a function of position y along the y axis.

c) Assume that d = 2m and the speed of sound = 360 m/s. Find the lowest speaker frequency which will yield the minimum sound intensity along the line BB'.

I wouldn't want someone to do these questions for me, however, I do want some pointers as to what fundamental equations I should be looking at and what topics to study.

I appreciate any help I get! THANKS!

 

[Hootenanny]

For question (a), if you assume they are moving at a constant velocity (the given 0.8c) you will have to take into account the time dilation effect because the muon is traveling relatively close to the spead of light. The formula for which is;

$$T = \frac{T_{0}}{\sqrt{1-\frac{v^2}{c^2}}}}$$

You might want to take a look at this page;
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html#c2

(b) is along the same lines. HINT: Your answer to a and b should be different.
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For the sound questions, you need to think about interference patterns, conditions for constructive / destructive interference etc.

Regards,
-Hoot