Question

Consider the situation shown in figure. The wire which has a mass of 4.00 g oscillates in its second harmonic and sets the air column in the tube into vibrations in its fundamental mode. Assuming that the speed of sound in air is 340 $m{s}^{-1}$, find the tension in the wire.

• A. 11.6N
• B. 340N
• C. 8 N
• D. None of these

Answer 1

The correct option is A

11.6N

Let T = tension of the string

$L=40cm=0.4m,m=4g=4\times {10}^{-3}kg$

$\frac{Mass}{length}\left(\mu \right)={10}^{-2}$

Fundamental frequency = $f_0=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

So, 2^nd harmonic $f_0=\frac{2}{2L}\sqrt{\frac{T}{\mu }}$

As it is unison with fundamental frequency of vibration in the air column

$\frac{\lambda }{4}=L$

$f=\frac{v}{4L}$

$f=\frac{340}{4\times L}=85Hz$

$\Rightarrow =\frac{2}{2\times 0.4}\sqrt{\frac{T}{10}}\Rightarrow T={85}^{2}x(0.4{)}^2\times {10}^{-2}=11.6N$.