Question

The equation of a standing wave, produced on a string fixed at both ends, is

$y=\left(0.4cm\right)sin\left[\right(0.314c{m}^{-1}\left)\right]cos\left[\right(600\pi s^{-1}\left)\right]$.

What could be the smallest length of the string ?

Answer 1

The equation of the standing wave is given by,

$y=\left(0.4cm\right)sin\left[\right(0.314c{m}^{-1}\left)x\right]cos\left[\right(600\pi s^{-1}\left)t\right]$

$\Rightarrow k=0.314=\frac{\pi }{10}$

$\Rightarrow L=20CM$

For smallest length of the string, as wavelength remains constant, the string should vibrate in fundamental frequency.

$\Rightarrow L=\frac{\lambda }{2}=20cm/2=10cm$