The ratio of the frequencies of the first ove | vedclass

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(D) For an open pipe of length $L$,the fundamental frequency is $f_{open, 1} = \frac{v}{2L}$. The first overtone is the second harmonic,given by $f_{o

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(D) For an open pipe of length $L$,the fundamental frequency is $f_{open, 1} = \frac{v}{2L}$. The first overtone is the second harmonic,given by $f_{open, 2} = 2 	imes f_{open, 1} = 2 	imes \frac{v}{2L} = \frac{v}{L}$.For a closed pipe of length $L$,the fundamental frequency is $f_{closed, 1} = \frac{v}{4L}$. The first overtone is the third harmonic,given by $f_{closed, 2} = 3 	imes f_{closed, 1} = 3 	imes \frac{v}{4L} = \frac{3v}{4L}$.The ratio of the frequency of the first overtone of the open pipe to that of the closed pipe is $\frac{f_{open, 2}}{f_{closed, 2}} = \frac{v/L}{3v/4L} = \frac{1}{1} 	imes \frac{4}{3} = \frac{4}{3}$.

The ratio of the frequencies of the first overtone produced by an open pipe to that of a closed pipe having the same length is

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