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Fundamental Harmonics on a String (Grades 11-12)

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Fundamental Harmonics on a String

Instructions: Read each question carefully. Choose the answer that best fits the question. Short answer response questions must be responded to in complete sentences. If the question involves calculations, you must show all your math work.

Use the image below as a visual aid to answering the questions.
Harmonics of a Vibrating String
Going from the top to the bottom of the image, identify the harmonic of sound for each string.

How many nodes and antinodes are there on the 5th harmonic?

What is the frequency of the third harmonic, if its fundamental frequency is 17 Hz?
  1. 5.67Hz
  2. 0.18Hz
  3. 17Hz
  4. 51Hz
What is the equation for finding the frequency of a harmonic of sound? Explain what the variables represent as part of your answer.

When a guitar string is plucked normally, the ear tends to hear the                                                  most prominently, the lowest frequency of vibration along the entire length of the string.
If the eighth harmonic has a frequency of 93 Hz, find the fundamental frequency. Show all your process in determining the answer.

If the frequency of a harmonic is 105Hz and its fundamental frequency is 26.25Hz, what is the number of the harmonic?

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