Physics - Wave on String Question with Solution | TestHub

For a string fixed at both ends, nodes are formed at the two ends.

If the string vibrates in $n$ loops, the total number of nodes formed is $n+1$.

Given that the total number of nodes is $X$, we have:

$X=n+1$

$n=X-1$

The length of the string $L$ in terms of wavelength $\lambda$ for $n$ loops is given by:

$L=n\frac{\lambda }{2}$

Substituting the value of $n$, we get:

$L=(X-1)\frac{\lambda }{2}$

Answer: $(\mathrm{X}-1)\frac{\lambda }{2}$