Stationary waves

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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

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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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Stationary waves

Remember concepts with our Masterclasses.

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

Second Harmony of wire : f2=22lTμ =1lTm/l=10.4T4×10−30.4=2.5100T=25T Fundamental frequency of closed pipe : f1=V4L=3404×1=85 During unison, f2=f1 ⇒25T=85 ⇒T=1752=3.42=11.56N

Ready to Test Your Skills?

free study material

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