WAVES

Ans. Formation of stationary waves in open pipe:- If both ends of the tube are opened thenit is known as an open organpipe.When a sound waveis sent through a pipe from one open end it gets reflected from the other open end due topressure difference.Anti nodes are formed at the two openends and a node is between them. Frequencies of Harmonicsin open pipes:

In the open pipe,while vibrating the length of the air column $L$ is equal to the multiple of integer number $n$ of ahalf wavelength

$$L=\frac{n\lambda}{2}$$

Wave length $\lambda=\frac{2L}{n}$

Frequency $\nu_{_n}=\frac{V}{\lambda}$
$$\nu_{_n}=\frac{nV}{2L} $$

$n=1$ then frst harmonic $\nu_{_1}=\frac {V}{2L} $

$n=2$ then second harmonic $\nu_{_2}=\frac{2V}{2L} =2\mathbf{\nu}_{_1}$

$n=3$ then third harmonic $\nu_{_3}=\frac{3V}{2L} =3\mathbf{\nu}_{_1}$

$$\nu_{_1}:\mathrm{\nu}_{_2}:\nu_{_3}=1:2:3$$