Deathslayer7

2009-10-22, 12:42 PM

A radar tower sends out a signal of wavelength lambda. It is x meters tall, and it stands on the edge of the ocean. A weather balloon is released from a boat that is a distance d out to sea. The balloon floats up to an altitude h. In this problem, assume that the boat and balloon are so far away from the radar tower that the small angle approximation holds.

Due to interference with reflections off the water, certain wavelengths will be weak when they reach the balloon. What is the maximum wavelength that will interfere destructively?

Express your answer in terms of x, h, and d.

Picture:

http://i198.photobucket.com/albums/aa125/death_slayer7/physics.jpg

where the orange line is the first wavelength, the blue line is the second wavelength which reflects off the water, but also a part goes through.

The black square is the radio tower, and the circle the hot air ballon.

my work:

I extend the second wavelength, so it touched down (h+x) length while the first is (h-x) length.

From there i proceeded to find the length difference and set it equal to lambda/2.

for L1(the orange) i got

L1^2= h^2 + 2*h*x+x^2+d^2

L2^2= h^2 - 2*h*x +x^2 +d^2

take the sqrt of both and subtract L1 from L2 you get this:

L2-L1= sqrt(h^2 + 2*h*x+x^2+d^2) - sqrt(h^2 - 2*h*x +x^2 +d^2)=lambda/2

Due to interference with reflections off the water, certain wavelengths will be weak when they reach the balloon. What is the maximum wavelength that will interfere destructively?

Express your answer in terms of x, h, and d.

Picture:

http://i198.photobucket.com/albums/aa125/death_slayer7/physics.jpg

where the orange line is the first wavelength, the blue line is the second wavelength which reflects off the water, but also a part goes through.

The black square is the radio tower, and the circle the hot air ballon.

my work:

I extend the second wavelength, so it touched down (h+x) length while the first is (h-x) length.

From there i proceeded to find the length difference and set it equal to lambda/2.

for L1(the orange) i got

L1^2= h^2 + 2*h*x+x^2+d^2

L2^2= h^2 - 2*h*x +x^2 +d^2

take the sqrt of both and subtract L1 from L2 you get this:

L2-L1= sqrt(h^2 + 2*h*x+x^2+d^2) - sqrt(h^2 - 2*h*x +x^2 +d^2)=lambda/2