A standing wave is produced on a string fixed at one end and free at the other. The length of the string
A standing wave is produced on a string fixed at one end and free at the other. The length of the string
must be an odd integral multiple of $\frac{\lambda}{4}$
must be an integral multiple of $\frac{\lambda}{2}$
must be an integral multiple of $\lambda$
may be an integral multiple of $\frac{\lambda}{2}$
Solution
The standing wave can be shown as
[Diagram shows fixed-free standing wave modes with lengths $\lambda/4$ and $3\lambda/4$.]
$\therefore$ The length of the string must be an odd multiple of $\frac{\lambda}{4}$.