The pipe open at both ends and pipe closed at one end have same length and both are vibrating in fundamental mode. Air column vibrating in open pipe has resonance frequency n 1 and air column vibrat

Question

The pipe open at both ends and pipe closed at one end have same length and both are vibrating in fundamental mode. Air column vibrating in open pipe has resonance frequency n 1 ​ and air column vibrating in closed pipe has resonance frequency n 2 ​ , then

TestHub · Accepted Answer

The fundamental frequency of a pipe open at both ends of length $L$ is given by $n_{1} = \frac{v}{2 L}$

The fundamental frequency of a pipe closed at one end of length $L$ is given by $n_{2} = \frac{v}{4 L}$

Taking the ratio of the two frequencies, we get:

$\frac{n _{1}}{n _{2}} = \frac{\frac{v}{2 L}}{\frac{v}{4 L}} = 2$

Thus, $n_{1} = 2 n_{2}$

Answer: $n_{1} = 2 n_{2}$

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