Physics - Wave on String Question with Solution | TestHub

The average power transmitted by a sinusoidal wave on a string is $P=\frac{1}{2}\mu A^2{\omega }^{2}v$, where $v=\sqrt{T/\mu }$. Substituting $v$, we get $P=\frac{1}{2}\mu A^2{\omega }^2\sqrt{T/\mu }=\frac{1}{2}{A}^2{\omega }^2\sqrt{\mu T}$. This shows $P\propto A^2{\omega }^2$, so Statement-1 is true. If $T$ is quadrupled ($T^{\prime }=4T$), then $P^{\prime }=\frac{1}{2}{A}^2{\omega }^2\sqrt{\mu (4T)}=2\left(\frac{1}{2}{A}^2{\omega }^2\sqrt{\mu T}\right)=2P$. So, power increases by a factor of 2, making Statement-2 true. Statement-2 is a consequence of the power formula but not an explanation for Statement-1.