Question

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

Answer 1

Answer: 10.00

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,
$\lambda =\frac{2\pi }{0.314}=\frac{2\times 3.14}{0.314}=20cm$
$\ell =\frac{\lambda }{2}=\frac{20}{2}=10cm$