Question

The figure shows a snap photograph of a vibrating string at t = 0. The particle P is observed moving with velocity $20\pi cm/s$ The angle made by string with x-axis at P is $6^o$ the total energy carried by the wave per cycle of the string, assuming that $\mu$, the mass per unit length of the string = 50 gm/m.

• A. $144{\pi }^2\times {10}^{-5}J$
• B. $121{\pi }^2\times {10}^{-5}J$
• C. $144{\pi }^3\times {10}^{-5}J$
• D. $144{\pi }^2\times {10}^{-4}J$

Answer 1

The correct option is A $144{\pi }^2\times {10}^{-5}J$

Here $A=4\times {10}^{-3}m$

$w=300\pi$ $\lambda =4\times {10}^{-2}m$

$\mu =50\times {10}^{-3}kg/m.$

For one cycle, $M=\mu \lambda =50\times {10}^{-3}\times 4\times {10}^{-2}$

$=200\times {10}^{-5}kg$

Total Energy$=\frac{1}{2}M{w}^2{A}^2$

$=\frac{1}{2}\times 200\times {10}^{-5}\times 900M^2\times 100\times 16\times {10}^{-6}$

$=144{\pi }^2\times {10}^{-5}J$