Rankers Physics

Standing Wave in String and Organ Pipe: Practice Problem & Solution

The length of the string of a musical instrument is $90 \text{ cm}$ and has a fundamental frequency of $120 \text{ Hz}$. Where should it be pressed to produce fundamental frequency of $180 \text{ Hz}$? (2020-Covid)
$60 \text{ cm}$
$45 \text{ cm}$
$80 \text{ cm}$
$75 \text{ cm}$

Solution Explained:

To solve this problem, we apply the core principles of Standing Wave in String and Organ Pipe. Understanding the underlying formula is key to arriving at the correct answer below:

Fundamental frequency $f \propto \frac{1}{L}$. So $f_1 L_1 = f_2 L_2$. $120 \times 90 = 180 \times L_2 \Rightarrow L_2 = 60 \text{ cm}$.

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