Question

A wave moving with constant speed on a uniform string passes the point $x=0$ with amplitude $A_0$, angular frequency ${\omega }_0$ and average rate of energy transfer $P_0$. As the wave travels down the string it gradually loses energy and at the point $x=\ell$, the average rate of energy transfer becomes. At the point $x=\ell$, angular frequency and amplitude are respectively:

• A. ${\omega }_0$ and $\frac{A_0}{\sqrt{2}}$
• B. $\frac{{\omega }_0}{\sqrt{2}}$ and $A_0$
• C. less than ${\omega }_0$ and $A_0$
• D. $\frac{{\omega }_0}{\sqrt{2}}$ and $\frac{A_0}{\sqrt{2}}$

Answer 1

Answer: (A)

$P=\frac{1}{2}\mu {\omega }^2{A}^{2}V$ and $v=\sqrt{\frac{T}{\mu }}$ will not change as both $T$ and $\mu$ are constant. $\omega$ will also not change as it is property of the source only that is causing the wave motion. Hence to make power half the amplitude becomes $\frac{A_0}{\sqrt{2}}$.