First slide

Stationary waves

Question

Consider the situation shown in fig. The wire which has a mass of 4.00g oscillates in its second harmonic and sets the air column in the tube into vibrations in its fundamental mode assuming the speed of sound in air is $340 m / \sec$ then the tension in the wire is ___________N

Moderate

Solution

$S e c o n d H a r m o n y o f w i r e : f_{2} = \frac{2}{2 l} \sqrt{\frac{T}{μ}} = \frac{1}{l} \sqrt{\frac{T}{m / l}} = \frac{1}{0.4} \sqrt{\frac{T}{\frac{4 \times 10^{- 3}}{0.4}}} = 2.5 \sqrt{100 T} = 25 \sqrt{T} F u n d a m e n t a l f r e q u e n c y o f c l o s e d p i p e : f_{1} = \frac{V}{4 L} = \frac{340}{4 \times 1} = 85 D u r i n g u n i s o n, f_{2} = f_{1} \Rightarrow 25 \sqrt{T} = 85 \Rightarrow T = {(\frac{17}{5})}^{2} = {(3.4)}^{2} = 11.56 N$

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