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PHXI15:WAVES

355203 A stretched string fixed at both ends has ' $m$ ' nodes then the length of the string will be

(m - 1) \frac{λ}{2}

\frac{(m + 1) λ}{2}

\frac{m λ}{2}

(m - 2) \frac{λ}{2}

Explanation:

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

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