A pipe open at both ends has a length of 1 ,m | vedclass

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(B) For a pipe open at both ends, the resonant frequencies are given by the formula: $f_n = \frac{n v}{2L}$, where $n = 1, 2, 3, \dots$ is the harmoni

Vedclass · Accepted Answer

$85$

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(B) For a pipe open at both ends, the resonant frequencies are given by the formula: $f_n = \frac{n v}{2L}$, where $n = 1, 2, 3, \dots$ is the harmonic number, $v$ is the speed of sound, and $L$ is the length of the pipe.Given: $v = 340 \,m/s$ and $L = 1 \,m$.Substituting these values, we get: $f_n = \frac{n 	imes 340}{2 	imes 1} = n 	imes 170 \,Hz$.This means the pipe can resonate at frequencies that are integer multiples of $170 \,Hz$ (i.e., $170 \,Hz, 340 \,Hz, 510 \,Hz, \dots$).Comparing this with the given options, $85 \,Hz$ is not a multiple of $170 \,Hz$ and therefore the air column cannot resonate at this frequency.

$A$ pipe open at both ends has a length of $1 \,m$. The air column in the pipe cannot resonate for which of the following frequencies (in $\,Hz$)? (Neglect end correction, speed of sound in air $= 340 \,m/s$)

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