Standing Waves Theory Question

In summary, by applying just enough mass to a standing wave, four "loops" or harmonics will be visible. If the mass density of the string were to double, no additional loops would be visible. However, if the mass density were to quadruple, only two loops would be visible. The formula used to calculate this is unknown, but the experiment involved changing the tension of the string with varying masses to produce different harmonics.
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Suppose that you were to apply just enough mass so that four "loops" (harmonics) are visible on a standing wave. If the mass density of the string were to double, how many loops (harmonics) if any would be visible? What about if the mass density were to quadruple? Explain.



This was a lab that I conducted for my Physics class. I know I need to use a formula to figure it out, but which one? Also, this standing wave is in between two fixed points with a consistent frequency being omitted. We just changed the tension of the string by hanging different masses on the one end so that we would get different amounts of harmonics to be shown.
 
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Anyone?? I can't figure it out!
 

What is standing wave theory?

Standing wave theory is a concept in physics that describes the phenomenon of a wave that appears to be stationary or "standing" in a certain location. This is created when two waves with the same frequency and amplitude travel in opposite directions and interact with each other.

What is the difference between standing waves and traveling waves?

The main difference between standing waves and traveling waves is that standing waves do not travel, they appear to be stationary. Traveling waves, on the other hand, move through space and transfer energy as they propagate. Additionally, standing waves are created by the interaction of two waves, while traveling waves are created by a single disturbance.

What are the applications of standing wave theory?

Standing wave theory has many practical applications, including musical instruments, such as stringed instruments and wind instruments. It is also used in telecommunications and radar technology to create and detect standing waves to transmit information.

How are standing waves formed?

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

What is the significance of nodes and antinodes in standing wave theory?

Nodes and antinodes are important components of standing waves. Nodes are points of no displacement, where the two waves cancel each other out, while antinodes are points of maximum displacement, where the two waves reinforce each other. These points help to define the standing wave pattern and determine the frequency of the wave.

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