WAVES

Ans. Formation of stationary waves in a closed pipe:-. If one end of a pipe is closed and another end is opened,thatpipe is called a closed pipe.

Explanation: When a sound wave is sent through an closed organ pipe the wave gets reflected at the end of the pipe. These incident and reflected waves having same frequency travelling in the opposite directions are superimposed along the length of thepipe andform alongitudinal stationary wave.At theopen end always an antinode and at the closed end always node is formed

Frequencies of Harmonics in closed pipes: In the closed pipe,while vibrating the length of the air column‘L'is equal to the

multiple of odd number $(2\mathbf{n}+1)\frac{\lambda}{4}$ of a quarter of wavelength

$$L=(2\mathbf{n}+1)\frac{\lambda}{4}$$

Wave length $\lambda=\frac{4L}{(2\mathbf{n}+1)}$

Frequency $\nu_{_n}=\frac{V}{\lambda}$
$$\nu_{_n}=(2\mathbf{n}+1)\frac{V}{4L} $$

$n=0$ then fundamental frequency $\nu_{_{\circ}}=\frac {V}{4L} $

$n=1$ then first Overtone  $\nu_{_1}=\frac{3V}{4L} =2\mathbf{\nu}_{_{\circ}}$

$n=2$ thenSecond Overtone  $\nu_{_2}=\frac{5V}{4L} =3\mathbf{\nu}_{_{\circ}}$

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