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  4. The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by y=2 cm sin [(0.6 cm -1) x] cos [(500 π s-1) t]The length of the string is:

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Q. The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by $y=2\, cm$ $\sin \left[\left(0.6\, cm ^{-1}\right) x\right] \cos \left[\left(500 \pi s^{-1}\right) t\right]$The length of the string is:

Waves

Solution:

Wave number $K=\frac{2 \pi}{\lambda}=0.6\, cm ^{-1}$
$\therefore \frac{\lambda}{2}=\frac{\pi}{0.6} cm$
$\therefore l=\frac{3 \lambda}{2}=3\left(\frac{\pi}{0.6}\right) cm$
$=15.7\, cm$