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An organ pipe of length L open at both e...

An organ pipe of length L open at both ends is found to vibrate in its harmonic when sounded with a tuning fork of 480Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?

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To solve the problem, we need to find the length of a pipe closed at one end (let's call it \( L_2 \)) that will vibrate in its first harmonic with a frequency of 480 Hz, given that a pipe open at both ends (length \( L_1 \)) also vibrates at the same frequency. ### Step-by-step Solution: 1. **Understanding the Harmonics of Open and Closed Pipes**: - For a pipe open at both ends, the first harmonic (fundamental frequency) has a wavelength \( \lambda_1 \) related to the length \( L_1 \) by the formula: \[ L_1 = \frac{\lambda_1}{2} ...
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