Question on standing/stationary waves

[pianogirl]

Homework Statement

Two navigation beacons 60km apart transmit radio waves of wavelength 4000m. The signals start with the same phase and amplitude. A ship is midway between them and is sailing straight towards one of them. Describe what happens to the signals received on board the ship over the next 6km.

Homework Equations

v=f x lambda ?

The Attempt at a Solution

Um... I just don't really get it...
I was thinking along the lines that there would 15 waves in the 60km...?

 

[Delphi51]

The two sources create a pattern of constructive and destructive interference.
You could draw it with a compass or take a look at a simulation - there are many on the web like this one: http://www.ngsir.netfirms.com/englishhtm/Interference.htm

 

[kerimek]

I can provide a response to this question by explaining the concept of standing/stationary waves. When two waves of the same frequency and amplitude travel in opposite directions, they can create a standing or stationary wave. This means that the wave appears to be standing still, with certain points called nodes and antinodes remaining stationary.

In this scenario, the two navigation beacons are transmitting radio waves of the same wavelength and starting with the same phase and amplitude. As the ship travels towards one of the beacons, it will experience a change in the received signals due to the formation of a standing wave.

As the ship moves towards the beacon, it will pass through multiple nodes and antinodes, resulting in a change in the received signal. This change will occur every half-wavelength, which in this case is 2000m. So, in the first 6km, the ship will pass through 3 half-wavelengths, resulting in 3 changes in the received signal.

In terms of the number of waves, the ship will pass through 3 full waves in the first 6km, as each full wave has 2 half-wavelengths. This means that the ship will experience a gradual increase in the amplitude of the received signal as it gets closer to the beacon, due to the constructive interference at the antinodes.

In summary, as the ship travels towards one of the beacons, it will experience a change in the received signals due to the formation of a standing wave, passing through multiple nodes and antinodes. This can be explained by the concept of constructive and destructive interference, resulting in changes in the amplitude of the received signal.