Question

Consider the situation shown in figure (16-E9). 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 $340m{s}^{-1}$, find the tension in the wire.

Answer 1

Let n_0 =frequency of the tuning for k,

T=tension of the string

L=40 cm =0.4 m, m =4g

$=4\times {10}^{-3}kg$

So, $m=\frac{\text{Mass}}{\text{Unit length}}={10}^{-2}kg/m$

$n_0=\frac{1}{2L}\sqrt{\frac{T}{m}}$

So, $2^{nd}$ Harmonic $2n_0=\left(\frac{2}{2L}\right)\sqrt{\frac{T}{m}}$

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

$\Rightarrow 2n_0=\frac{340}{4}\times 1=85Hz$

$\Rightarrow 85=\frac{2}{2\times 0.4}\sqrt{\frac{T}{14}}$

$=T=(84{)}^2\times (0.4{)}^2$

=11.6 Newton