Question

The equation of a standing wave, produced on a string fixed at both ends, is
y=(0·4 cm) sin [(0·314 cm-1) x] cos [(600π s-1) t].
What could be the smallest length of the string?

Answer 1

The Smallest Length Could be 20 cm

Explanation:

The Equation of the standing wave is given by -

*Refer diagram as attached file

y = $(0.4\ cm) sin[(0.314 cm^-^1)x]cos [(6.00 \pi s^-^1)t]$

⇒ k = 0.314 = $\frac {\pi}{10}$

⇒ $\frac {2\pi}{\lambda} = \frac {\pi}{10}$

= $\lambda = 20 cm$

For smallest length of the string, as wavelength remains constant, the string should vibrate in fundamental frequency => l = \lambda/2 = 20 cm / 2 = 10 cm.