A tuning fork of frequency 340, Hz is vibrate | vedclass

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Question

(A) The wavelength $\lambda$ of the sound wave is given by $\lambda = \frac{v}{f} = \frac{340\, m/s}{340\, Hz} = 1\, m = 100\, cm$.The resonant length

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(A) The wavelength $\lambda$ of the sound wave is given by $\lambda = \frac{v}{f} = \frac{340\, m/s}{340\, Hz} = 1\, m = 100\, cm$.The resonant lengths $l$ for a tube closed at one end are given by $l = \frac{(2n-1)\lambda}{4}$ for $n = 1, 2, 3, \dots$.For $n=1$,$l_1 = \frac{\lambda}{4} = \frac{100\, cm}{4} = 25\, cm$.For $n=2$,$l_2 = \frac{3\lambda}{4} = \frac{3 	imes 100\, cm}{4} = 75\, cm$.For $n=3$,$l_3 = \frac{5\lambda}{4} = \frac{5 	imes 100\, cm}{4} = 125\, cm$.Since the tube height is $120\, cm$,only $l_1 = 25\, cm$ and $l_2 = 75\, cm$ are possible.To find the minimum height of water,we need the maximum possible air column length for resonance,which is $l_2 = 75\, cm$.Minimum height of water $= 	ext{Total height} - l_2 = 120\, cm - 75\, cm = 45\, cm$.

$A$ tuning fork of frequency $340\, Hz$ is vibrated just above a tube of $120\, cm$ height. Water is poured slowly into the tube. What is the minimum height of water necessary for resonance? (Speed of sound in air $= 340\, m/s$)

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