Question

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

• A. less than ${\omega }_0$ and $A_0$
• B. $\frac{{\omega }_0}{\sqrt{2}}$
• C. $\frac{{\omega }_0}{\sqrt{2}}$ and $\frac{A_0}{\sqrt{2}}$
• D. ${\omega }_{0}and\frac{A_0}{\sqrt{2}}$
  

Answer 1

The correct option is D ${\omega }_{0}and\frac{A_0}{\sqrt{2}}$


As we know,
$P=\frac{1}{2}\mu {\omega }^2{A}^2$ 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 $\frac{A_0}{\sqrt{2}}$
Final answer: (a)