# Question on standing/stationary waves

• pianogirl
In summary, two navigation beacons 60km apart emit radio waves with the same phase and amplitude. A ship sailing straight towards one of them experiences constructive and destructive interference, resulting in a pattern of 15 waves over a distance of 6km. This can be visualized using a compass or a simulation.
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.

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...?

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

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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.

## 1. What are standing/stationary waves?

Standing/stationary waves are a type of wave pattern that occurs when two identical waves with the same frequency and amplitude travel in opposite directions, interfering with each other. This results in areas of constructive and destructive interference, causing the wave to appear to be standing still.

## 2. What is the difference between standing and stationary waves?

Standing and stationary waves are often used interchangeably, but technically, there is a slight difference. Standing waves refer to the physical appearance of the wave, while stationary waves refer to the mathematical representation of the wave.

## 3. How are standing/stationary waves formed?

Standing/stationary waves are formed by the superposition of two waves with the same frequency and amplitude traveling in opposite directions. This causes the interference pattern to form, resulting in areas of constructive and destructive interference that make the wave appear to be standing still.

## 4. What is the significance of standing/stationary waves?

Standing/stationary waves have many practical applications, such as in musical instruments, antennas, and earthquake detection. They also help scientists understand the properties of waves and how they behave in different environments.

## 5. How do standing/stationary waves differ from other types of waves?

Unlike other types of waves that travel through a medium, standing/stationary waves do not actually transfer energy from one point to another. Instead, they oscillate in place, with the energy being constantly reflected back and forth between the points of constructive interference.

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