# Problem of Interference

#### ick24

1. The problem statement, all variables and given/known data

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

#### Redbelly98

Staff Emeritus
Homework Helper
Re: Interference

Welcome to Physics Forums.

1. The problem statement, all variables and given/known data

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
The radio towers are acting like the two slits, in that they are a source of waves that can interfere. The tower seperation 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

Re: Interference

seriously that didn't help..but thanks

#### Redbelly98

Staff Emeritus
Homework Helper
Re: Interference

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

Re: Interference

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

Staff Emeritus
Homework Helper
Re: Interference

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

Re: Interference

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

Re: Interference

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"

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#### Redbelly98

Staff Emeritus
Homework Helper
Re: Interference

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:

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

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#### ick24

Re: Interference

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

Staff Emeritus
Homework Helper
Re: Interference

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

Re: Interference

I understand whats 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

Staff Emeritus
Homework Helper
Re: Interference

I understand whats 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

Re: Interference

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

Staff Emeritus
Homework Helper
Re: Interference

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

Staff Emeritus
Homework Helper
Re: Interference

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] [Broken]

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.​

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#### ick24

Re: Interference

y=$$\lambda$$D/a
is that the maximum signal strength

#### Redbelly98

Staff Emeritus
Homework Helper
Re: Interference

y=$$\lambda$$D/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.

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