Question

A tuning fork is used above a open tube and the 1st harmonic happens at 7 cm. Where will the 5th harmonic be heard?

Answer 1

Let the 5th harmonic will be heard at $\lambda_{5}$ .

The wavelength of the 1st harmonic is $\lambda$ =7 cm.

Let the length of the open tube is L.

We know for 1st harmonic

  $L=\frac{1}{2}\lambda$

Now we know for 5th harmonic

$\lambda _{5}=\frac{2}{5}L$

   $or\: \: \: \: \: \: \: \lambda _{5}=\frac{2}{5}\times \left ( \frac{1}{2} \lambda \right )$

$or\: \: \: \: \: \: \: \lambda _{5}=\frac{2}{5}\times \left ( \frac{1}{2} \times 7 \right )$

  $\therefore \: \: \: \: \: \: \: \lambda _{5}=1.4\: \: \: \: \: cm$

$\therefore$ The 5th harmonic will be heard at 1.4 cm.