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A 4 loop standing wave on a string that is 2 meters long oscialltes at a frequency of 6.7 Hz. What woud be the frequency of the string if it had an 8 loop standing wave pattern?

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The frequency of the string if it had an 8 loop standing wave pattern is determined as 13.4 Hz.

Relationship between number of loops and harmonics

The relationship between number of loops and harmonics of the standing wave is given as follows;

  • 1 loop = first harmonic = f₁
  • 2 loops = second harmonic = f₂ = 2f₁
  • 3 loops = third harmonic = f₃ = 3f₁
  • 4 loops = fourth harmonic = f₄ = 4f₁
  • 8 loops = eight harmonic = f₈ = 8f₁

Frequency of the string if it had an 8 loops standing wave pattern

f₄ = 4f₁

f₁ = f₄/4

f₈ = 8f₁

f₈ = 8(f₄/4)

f₈ = 2f₄

f₈ = 2 x 6.7 Hz

f₈ = 13.4 Hz

Thus, the frequency of the string if it had an 8 loop standing wave pattern is determined as 13.4 Hz.

Learn more about frequency here: https://brainly.com/question/10728818

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