91Ó°ÊÓ

Mass of string \(m = 6.00\;{\rm{g}}\).

Length of string \(L = 8.00\;m\)

Speed of wave \(v = 30.0\;{\rm{m/s}}\).

Wavelength is \(\lambda = 0.2\;{\rm{m}}\)

The formula of power is:

\(\begin{array}{l}P = \rho {\omega ^2}{A^2}Sv\\A = \frac{1}{\omega }\sqrt {\frac{{2P}}{{\rho Sv}}} \end{array}\).

Here,\(\rho S = \mu \)is mass per unit length.

The angular velocity is calculated as follows:

\(\begin{array}{c}\omega = 2\pi f\\ = \frac{{2\pi v}}{\lambda }\\ = \frac{{2\pi }}{{0.2}} \times 30\end{array}\)

Also, calculate the mass per unit length as follows:

\(\begin{array}{c}\mu = \rho S\\ = \frac{{6 \times {{10}^{ - 3}}}}{8}{\rm{kg/m}}\end{array}\)

Substitute these values in the formula of amplitude of the wave gives:

\(\begin{array}{c}A = \frac{{0.2}}{{2\pi \times 30}}\sqrt {\frac{{2 \times 50 \times 8}}{{6 \times {{10}^{ - 3}} \times 30}}} \\ = 0.0707\;m\\ = 7.07\;cm\end{array}\)

Thus, the amplitude of the wave is 7.07 cm.