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STT 16.4 A standing wave on a string is shown. Which of the models below has twice the frequency of the original wave?

User Shibi
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1 Answer

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Final answer:

The model representing a standing wave with twice the frequency of the original wave is the second harmonic or first overtone, which has one additional node compared to the fundamental frequency mode on a string fixed at both ends.

Step-by-step explanation:

The question is related to the standing waves on a string and their frequencies. When a string is plucked and a standing wave is formed, the first frequency at which a normal mode occurs is the fundamental frequency, also known as the first harmonic. The frequency doubles with each successive normal mode. Therefore, the model that represents a wave with twice the frequency of the original wave is going to be the second harmonic or first overtone. This is because the frequency of the n = 2 normal mode (first overtone) is twice that of the fundamental frequency (first harmonic). In a physical model with a string fixed at both ends, like in a guitar or a violin, this would look like the string having a single additional node compared to the fundamental frequency mode.

User Phiber
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