How Many Harmonics in a 4-Node Standing Wave?

In summary, standing waves are stationary wave patterns that occur when two waves with the same frequency and amplitude interfere with each other. Nodes, where the amplitude is always zero, are created through destructive interference. Standing waves are formed when two identical waves travel in opposite directions, and the wavelength is directly related to the number of nodes in the wave. These types of waves have practical applications in fields such as music, microscopy, and telecommunications.
  • #1
PearlyD
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Homework Statement


A standing wave is set on a string by a vibrating the string at one end. You count 4 nodes on the standing wave. Which harmonic have you produced?




The Attempt at a Solution


I thought it was 3rd harmonic,but my teacher put 2nd harmonic
whos right?
 
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  • #3


As a scientist, it is important to understand that both answers could be correct depending on the specific context of the situation. Generally, the harmonic refers to the number of complete wavelengths that can fit within the length of the string. In this case, if there are 4 nodes present, it is likely that the string can fit 2 full wavelengths, making it the 2nd harmonic. However, if the string was fixed at both ends and the 4 nodes were present, it could also be considered the 3rd harmonic. It is important to clarify the specific conditions and set-up of the experiment in order to determine the correct harmonic.
 

1. What is a standing wave?

A standing wave is a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This results in areas of constructive and destructive interference, creating a pattern of nodes and antinodes.

2. What are nodes in a standing wave?

Nodes are points in a standing wave where the amplitude of the wave is always zero. They occur at fixed positions along the wave and do not move as the wave travels. Nodes are areas of destructive interference where the two waves cancel each other out.

3. How are standing waves formed?

Standing waves are formed when two identical waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This creates areas of constructive and destructive interference, resulting in a stationary wave pattern.

4. What is the relationship between wavelength and the number of nodes in a standing wave?

The wavelength of a standing wave is directly related to the number of nodes in the wave. The distance between two consecutive nodes is equal to half of the wavelength of the wave. This means that as the wavelength increases, the number of nodes in the wave also increases.

5. How are standing waves used in real-world applications?

Standing waves have many practical applications, such as in musical instruments, where they are responsible for the production of different notes and harmonics. They are also used in various types of microscopy, such as scanning electron microscopy, to produce high-resolution images. Standing waves are also utilized in telecommunications, specifically in the design of antennas for wireless communication.

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