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Step 1:I'll solve this problem by providing a clear, step-by-step explanation of the fundamental frequency equation.
Step 2:: Define Fundamental Frequency
The fundamental frequency is the lowest frequency of a vibrating system, such as a string or air column. It represents the first harmonic or primary mode of vibration.
Step 3:: Fundamental Frequency Equation for a String
- $$\mu$$ is the linear mass density of the string
For a vibrating string, the fundamental frequency equation is: Where:
Step 4:: Fundamental Frequency Equation for an Air Column
- $$L$$ is the length of the air column
For an open-ended air column, the fundamental frequency is: Where:
Final Answer
1. For a string: f_{1} = \frac{1}{2L} \sqrt{\frac{T}{\mu}} 2. For an open-ended air column: f_{1} = \frac{v}{2L}
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