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  4. A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y = 0.3 sin(0.157 x) cos(200π t). The length of the string is: (All quantities are in SI units.)

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Q. A string is clamped at both the ends and it is vibrating in its $4^{th}$ harmonic. The equation of the stationary wave is $Y = 0.3 sin(0.157 x) cos(200\pi t$). The length of the string is : (All quantities are in SI units.)

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Solution:

4th harmonic
$4 \frac{\lambda}{2} = \ell$
$2 \lambda = \ell$
From equation $\frac{2 \pi}{\lambda} = 0.157$
$\lambda = 40$
$\ell = 2\lambda$
$= 80 m$
Option (2)

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