Interference of radio waves

In summary, the solution for the ship as a two point source emitter involves one point source above the water and one below. The one below is out of phase by half a wavelength to account for the reflection of radio waves off the water's surface. This results in a (1/2)λ phase shift for the waves. The path difference (d sin θ) also contributes to the phase shift, and for the waves to cancel out at the receiving station, the path difference must be equal to a multiple of the wavelength. This results in destructive interference and loss of radio contact between the ship and receiving station.
  • #1
48
5
Homework Statement
A ship approaching harbor is transmitting at a wavelength of λ = 3.43 m from its antenna located h = 23 m above sea level. The receiving station antenna is located H = 160 m above sea level. What is the horizontal distance D between ship and receiving tower when radio contact is momentarily lost for the first time? Assume that the calm ocean reflects radio waves perfectly according to the law of reflection. (diagram below)
Relevant Equations
d sin θ = (m + 1/2) λ
1669347268103.png

The solution pretends that the ship is a two point source emitter, one h above the water, and one h below the water.
The one below the water is out of phase by half a wavelength.

I don't understand why then d sin θ = λ - wouldn't it be d sin θ = (1/2)λ since it is out of phase?

Thank you.
 
Physics news on Phys.org
  • #2
jolly_math said:
I don't understand why then d sin θ = λ - wouldn't it be d sin θ = (1/2)λ since it is out of phase?
The two point sources emit out of phase. That is, the waves start out from the two sources already with a (1/2)λ phase shift. The path difference (d sin θ) contributes additional phase shift where the waves arrive at the receiving station. If the path difference is (1/2)λ, what would be the total phase shift? Would that yield constructive or destructive interference?
 
  • Like
Likes jolly_math and MatinSAR
  • #3
TSny said:
The two point sources emit out of phase. That is, the waves start out from the two sources already with a (1/2)λ phase shift. The path difference (d sin θ) contributes additional phase shift where the waves arrive at the receiving station. If the path difference is (1/2)λ, what would be the total phase shift? Would that yield constructive or destructive interference?
I'm confused by how "the one below the water is out of phase by half a wavelength" is derived from the question. Also, why is the path difference (1/2)λ?

When the question states that "radio contact is momentarily lost for the first time", is it looking for constructive or destructive interference?

Thank you.
 
  • #4
jolly_math said:
I'm confused by how "the one below the water is out of phase by half a wavelength" is derived from the question.
The underlying reason is that, when a radio wave reflects off of the surface of water, the radio wave undergoes a (1/2)λ phase shift. This is taken into account by taking the "phantom" underwater point source to be emitting waves that are (1/2)λ out of phase with the above water point source.

Did you discuss phase shifts due to reflection in class? There is a rule for deciding whether or not a light wave has a (1/2)λ phase shift due to reflection. It involves the indices of refraction of the two media where the reflection takes place. The same rule applies to radio waves.

[EDIT: In introductory physics courses, it is often stated that there will be a (1/2)λ phase shift at reflection if the ratio of the indices of refraction ##n_2/n_1## is greater than 1. Actually, there are exceptions to this that depend on the angle of incidence and the polarization of the waves. But, this is not usually covered in introductory classes. So, I guess that in this question you were just expected to assume that there will be a (1/2)λ phase shift due to reflection since ##n_2/n_1## is greater than 1 for an air-to-water interface.]

jolly_math said:
Also, why is the path difference (1/2)λ?
In the first post you asked, "I don't understand why then d sin θ = λ - wouldn't it be d sin θ = (1/2)λ since it is out of phase?"

I wanted you to see that if you take the path difference to be (1/2)λ, then the waves at the receiving station would not result in the receiving station losing contact with the ship. So, (1/2)λ path difference is not going to work.

jolly_math said:
When the question states that "radio contact is momentarily lost for the first time", is it looking for constructive or destructive interference?
The contact is lost because the waves from the two point sources "cancel out" at the receiving station. Would this be constructive or destructive interference?
 
Last edited:
  • Like
Likes berkeman and jolly_math
  • #5
TSny said:
The contact is lost because the waves from the two point sources "cancel out" at the receiving station. Would this be constructive or destructive interference?
This would be destructive interference. d sin θ = λ so that the overall phase difference is 1.5λ, which still ensures destructive interference - is this right?
 
  • Like
Likes berkeman
  • #6
jolly_math said:
This would be destructive interference. d sin θ = λ so that the overall phase difference is 1.5λ, which still ensures destructive interference - is this right?
Yes. Good.
 
  • Like
Likes jolly_math

1. What is interference of radio waves?

Interference of radio waves is the phenomenon where two or more radio waves interact with each other, causing changes in their amplitude, frequency, or phase. This can result in distortion or disruption of the original signals.

2. What causes interference of radio waves?

Interference of radio waves can be caused by a variety of factors, such as physical obstacles like buildings or trees, atmospheric conditions like thunderstorms, or other electronic devices emitting radio waves in the same frequency range.

3. How does interference affect radio communication?

Interference can disrupt or weaken radio signals, making it difficult for receivers to accurately interpret the transmitted information. This can result in poor audio or video quality, dropped calls, or complete loss of communication.

4. Can interference of radio waves be prevented?

While it is not possible to completely eliminate interference, there are measures that can be taken to minimize its effects. This includes using shielding materials, adjusting the frequency or direction of the radio waves, or using advanced signal processing techniques.

5. How does interference of radio waves impact scientific research?

Interference of radio waves can have a significant impact on scientific research that relies on precise and accurate measurements. It can introduce errors or distortions in data, making it difficult to draw accurate conclusions. Scientists must carefully consider and control for interference when conducting experiments involving radio waves.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
780
  • Introductory Physics Homework Help
Replies
1
Views
799
  • Introductory Physics Homework Help
Replies
20
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
7K
  • Introductory Physics Homework Help
Replies
1
Views
937
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
3K
  • Introductory Physics Homework Help
Replies
5
Views
871
  • Introductory Physics Homework Help
Replies
1
Views
1K
Back
Top