A cylindrical tube (L = 120,cm) is resonant w | vedclass

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(A) The frequency of the tuning fork is $f = 330\,Hz$ and the speed of sound is $v = 330\,m/s$.The wavelength is $\lambda = \frac{v}{f} = \frac{330}{3

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$45$

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(A) The frequency of the tuning fork is $f = 330\,Hz$ and the speed of sound is $v = 330\,m/s$.The wavelength is $\lambda = \frac{v}{f} = \frac{330}{330} = 1\,m = 100\,cm$.For a closed organ pipe (resonance tube),the resonance occurs when the length of the air column $l$ satisfies $l = \frac{(2n-1)\lambda}{4}$ for $n = 1, 2, 3, \dots$.Given the total length of the tube is $L = 120\,cm$,the length of the air column $l$ must be less than or equal to $120\,cm$.For $n=1$,$l_1 = \frac{\lambda}{4} = \frac{100}{4} = 25\,cm$.For $n=2$,$l_2 = \frac{3\lambda}{4} = \frac{300}{4} = 75\,cm$.For $n=3$,$l_3 = \frac{5\lambda}{4} = \frac{500}{4} = 125\,cm$ (which is greater than $120\,cm$,so this is not possible).The length of the water column $h$ is given by $h = L - l$.To get the minimum length of the water column,we need the maximum possible length of the air column $l$ that is $\le 120\,cm$.Thus,we take $l = 75\,cm$.The minimum water column length is $h = 120\,cm - 75\,cm = 45\,cm$.

$A$ cylindrical tube $(L = 120\,cm)$ is resonant with a tuning fork of frequency $330\,Hz$. If it is being filled with water,what is the minimum length of the water column required to achieve resonance? (Speed of sound in air $V_{air} = 330\,m/s$)

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