# Question #ce1a2

Jul 29, 2016

String will not form loops.

#### Explanation:

If we observe the formation of stationary wave forms of different frequencires or wave lentgths in the streched strings as shown in the given figure,we see that to produce a stationary wave the antinode is first created by plucking the string in such a way that intgral number of loops are formed in the whole length(l)of the streched string.

Now length of one loop is equal to half of wave length $\lambda$
So

$l = \frac{n \lambda}{2} , \text{where } n = 1 , 2 , 3. \ldots .$

Again the plucking of string should be done at a distance $d = \frac{\lambda}{4}$ from any end of the string.

So $l = \frac{n \lambda}{2} = \frac{2 n \lambda}{4} = 2 n d$

$\therefore d = \frac{l}{2 n}$

If $d = \frac{l}{3}$

then $\frac{l}{3} = \frac{l}{2 n} \implies n = \frac{3}{2} \to \text{Impossible}$

So to creat stationary wave $\textcolor{red}{l}$ must be even multiple of $\textcolor{b l u e}{d}$.