question_answer 46)

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

Answer:

                  In case of open ended pipe, the frequency of first harmonic is given by                 \[{{v}_{0}}=\frac{\upsilon }{2L}=480\,Hz\]                 For a closed end pipe, frequency of first harmonic is given by                     \[v'\,=\frac{\upsilon }{2L'}\,=\,480\,Hz\]                 \[\therefore \] \[\frac{{{v}_{c}}}{{{v}_{0}}}\,=\,\frac{\upsilon }{2L}\times \,\frac{4L'}{\upsilon }\,=\,\frac{2L'}{L}\]                 or \[L'\,=\frac{L}{2}\].