Question

A stretched string fixed at both ends has ${}^{\prime }{m}^{\prime }$ 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
$l=\frac{(m-1)\lambda }{2}$