What Factors Affect the Distance of Strong Signals in Radar Transmission?

[ick24]

Homework Statement

Two radar transmission towers located 6.4 km apart emit identical signals of wavelength 420
meters. A ship located at a point 30 km equidistant from the
towers experiences a strong signal from the towers. However,
as it sails parallel to the line of the towers it experiences an
alternating diminishing and re-strengthen of the signal strength.
a) Calculate the distance between the points of maximum
signal strength.
b) What would be the effect on the distance between strong
signals if:
i. The distance between the towers was decreased
ii. The ship was a greater distance away from the
towers
iii. The signals had a longer wavelength
c) Given that the wavelength of the signal emitted by the towers is 450m , then
i. What is its frequency?
ii. Name the frequency band this signal would classified as.


don't really see how this question is associated with Young's Double Slit Experiment
help please!

 

[Redbelly98]

Welcome to Physics Forums.

Homework Statement

Two radar transmission towers located 6.4 km apart emit identical signals of wavelength 420
meters. A ship located at a point 30 km equidistant from the
towers experiences a strong signal from the towers. However,
as it sails parallel to the line of the towers it experiences an
alternating diminishing and re-strengthen of the signal strength.
a) Calculate the distance between the points of maximum
signal strength.
b) What would be the effect on the distance between strong
signals if:
i. The distance between the towers was decreased
ii. The ship was a greater distance away from the
towers
iii. The signals had a longer wavelength
c) Given that the wavelength of the signal emitted by the towers is 450m , then
i. What is its frequency?
ii. Name the frequency band this signal would classified as.don't really see how this question is associated with Young's Double Slit Experiment
help please!

The radio towers are acting like the two slits, in that they are a source of waves that can interfere. The tower separation of 6.4 km is just like the distance between the two slits in Young's experiment.

So, you can use the same equation that describes interference in Young's double slit. (You should also draw yourself a figure, if you haven't already, so that you have a clear picture of the situation.)

 

[ick24]

seriously that didn't help..but thanks

 

[Redbelly98]

There should be a discussion, and an equation, for the double slit experiment in your textbook or lecture notes. Apply the equation that deals with the interference maximums (constructive interference, or bright fringes).

 

[ick24]

ok so i got the formula for calculating the bright fringes...i put in the variables and i get 65.6km but that still does not explain the signal strength

 

[Redbelly98]

ok so i got the formula for calculating the bright fringes...i put in the variables and i get 65.6km...

That doesn't look right, it should be something much smaller. What formula did you use exactly? Can you show your calculation?

... but that still does not explain the signal strength

Do you understand what constructive and destructive interference of two waves means? That is all that is going on here.

 

[ick24]

yes..i know that destructive interference is when a trough and a crest of 2 different met and cross out each other and constructive interference is when 2 waves forms of the same phase met and create a bigger wave

 

[Liquidxlax]

yes..i know that destructive interference is when a trough and a crest of 2 different met and cross out each other and constructive interference is when 2 waves forms of the same phase met and create a bigger wave

superposition check this link out maybe it will give you a better understanding

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=19"

 

[Redbelly98]

ok so i got the formula for calculating the bright fringes...i put in the variables and i get 65.6km but that still does not explain the signal strength

yes..i know that destructive interference is when a trough and a crest of 2 different met and cross out each other and constructive interference is when 2 waves forms of the same phase met and create a bigger wave

The signal strength is strongest where there is constructive interference, and weakest where the interference is destructive. In the figures below, S1 and S2 would be the radio tower locations, and O, P, and P1 are possible locations of the ship:

[PLAIN]http://upload.vipulg.com/Physics/483/Chapter%2020_files/Chapter%2020-23.png

[PLAIN]http://upload.vipulg.com/Physics/483/Chapter%2020_files/Chapter%2020-24.png

(Figures are from http://www.tutornext.com/expression-intensity-light/16035" .)

 

[ick24]

Guys i appreciate it and all but i sill can't get this.. i understand what constructive and destructive interference is but what does it have to with the signal strength

 

[Redbelly98]

The signal is carried by radio waves. The strength of the signal is related to the amplitude as detected at the ship's location, where the waves from the two transmitters add together to produce a signal in the ship's receiver.

The amplitude, and therefore the signal strength, is highest wherever the two waves are interfering constructively. I'm confused as to why this isn't apparent, as it is pretty straightforward stuff.

If you still don't get it, I don't think I can explain it any more plainly than what I have posted here. Sorry.

 

[ick24]

I understand what's is going on here...my problem is finding a formula to solve this..I have an exam next Monday and I need to know this...

 

[Redbelly98]

I understand what's is going on here...my problem is finding a formula to solve this..I have an exam next Monday and I need to know this...

What? Earlier you said you have a formula...

ok so i got the formula for calculating the bright fringes...i put in the variables and i get 65.6km but that still does not explain the signal strength

Can you show your work? What formula did you use earlier? There is a relatively simple formula for the double slit to use here. It should be in your class lecture notes or your textbook, and it can also be found via googling.

p.s. Our forum's policy is that you need to show your work before receiving help.

 

[ick24]

i only have 2 formulas
Constructive interference: r1 - r2 = m\λ ,m = 1,2,... Destructive interference:r1 - r2 = (m + 1\2)λ ,m = 1,2,...

 

[Redbelly98]

i only have 2 formulas
Constructive interference: r1 - r2 = m\λ ,m = 1,2,...

Destructive interference:r1 - r2 = (m + 1\2)λ ,m = 1,2,...

Okay. First a couple of corrections:

1. r1 - r2 = m·λ, not m\λ

2. m can be 0, as well as 1, 2,...

So how did you come up with 65.6 km before?

 

[Redbelly98]

Hey, I have found an image that shows the situation pretty clearly:

[PLAIN]http://www.wellesley.edu/Physics/phyllisflemingphysics/106_s_physoptics_images/figure_3.gif[/CENTER]

We know that r1 and r2 differ by λ, and there are two right triangles in the figure. The idea is to solve for y in terms of d and λ.​

 

[ick24]

y=\lambdaD/a
is that the maximum signal strength

 

[Redbelly98]

y=\lambdaD/a
is that the maximum signal strength

If D is the distance from the towers to the ship, and a is the distance between the two towers, then yes.