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  • An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz.

An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. 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?

Answers (1)

As the medium, number and frequency of harmonic in open and closed pipes are the same, so the number of nodes and wavelength in both cases will also be the same.

In both end open pipe

L_{1}=2\times \frac{\lambda _{1}}{4} or\lambda _{1}=2L_{1}

v_{1}=\frac{c}{\lambda _{1}}=\frac{c}{2L_{1}}

In one open end pipe

L_{2}=1\times \frac{\lambda _{2}}{4} or\lambda _{2}=4L_{2}

v_{2}=\frac{c}{4L_{2}}

v_{1}=v_{2} and c_{1}=c_{2}=c

 

\frac{c}{2L_{1}}=\frac{c}{4L_{2}}

Or \\4L_{2}=2L_{1} ;\\L_{2}=L_{1}/2

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infoexpert24

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