Question

Assertion :In a small segment of string carrying sinusoidal wave, total energy is conserved if system is isolated. Reason: Every small part moves in SHM.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

The Transmitted power at any point on the string (executing wave motion) is given by: P = $\frac{{\omega }^2{A}^{2}Fco{s}^2(\omega t-kx)}{v}$
The Total energy (up to time 't') = ${\int }_0^{t}Pdt$
The total energy varies with time (for each point), only the average Power delivered is independent of time. Hence the assertion is False. However energy for the entire string would be conserved.
From the wave equation
$y=A\sin (\omega t-kx)$
If we substitute a particular point (particular $x$), the equation becomes identical to that of a particle executing SHM.
Hence reason is true.