Question

A stretched string fixed at both ends has $'m'$ nodes, then the length of the string will be

• A. $\left(m-1\right) \frac{\lambda}{2}$
• B. $\frac{\left(m+1\right) \lambda}{2}$
• C. $\frac{m \lambda}{2}$
• D. $\left(m-2\right)\frac{ \lambda}{2}$

Answer 1

Answer: (A)

For $p$ number of loops in a stretched string, the length is given by
$l=\frac{p \lambda}{2} \,\,\,\,\,\,\,\,\,...(i)$
As, number of harmonics = number of loops = number of anti-nodes $= p \,\,\,\,\,\,\,\,...(i)$
Also, number of nodes $=$ number of anti-nodes $+1 $
Here, number of nodes $=m$
Number of anti-nodes $=m-1$
from Eq. (ii)
$p=m-1$
Putting this value of $p$ in Eq. (i), we get
$l=\frac{(m-1) \lambda}{2}$