Question

The equation of a standing wave produced on a string fixed at both the ends is $y=(0.4) \sin \left[\left(0.314 \,cm ^{-1}\right) x\right] \cos \left[\left(600\, \pi s^{-1}\right) t\right]$
What would be the smallest length of the string (in $cm$ ) ?

Answer 1

Both ends of strings are fixed, so both ends are node. So it looks as

So, possible smallest length
$\ell=\frac{\lambda}{2} $
$ k =\frac{2 \pi}{\lambda} ; \lambda=\frac{2 \pi}{ k }$
From equation,
$\lambda=\frac{2 \pi}{0.314}=\frac{2 \times 3.14}{0.314}=20 \,cm $
$\ell=\frac{\lambda}{2}=\frac{20}{2}=10\, cm$