Physics - Wave on String Question with Solution | TestHub

The average power transmitted by a wave on a string is given by $P_{avg}=\frac{1}{2}\mu A^2{\omega }^{2}v$. First, calculate the angular frequency $\omega =2\pi f=2\pi (100)=200\pi \text{ rad/s}$. The wave speed $v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{40}{0.1}}=\sqrt{400}=20\text{ m/s}$. Given amplitude $A=2.0\text{ cm}=0.02\text{ m}$. Substitute the values:$$P_{avg}=\frac{1}{2}(0.1\text{ kg/m})(0.02\text{ m}{)}^2(200\pi \text{ rad/s}{)}^2(20\text{ m/s})$$ $$P_{avg}=\frac{1}{2}(0.1)(0.0004)(40000{\pi }^2)(20)=16{\pi }^2\text{ W}$$