Question

A transverse wave is propagating through a medium. The potential energy associated with vibrating particle is maximum when the displacement of the particle from the mean position is

• A. Zero
• B. half of the amplitude
• C. equal to the amplitude
• D. none of the above

Answer 1

The correct option is C equal to the amplitude

We know that at mean position, velocity of particle is maximum.
$\Rightarrow$Hence kinetic energy associated with particle will be maximum at mean position.
Similarly,
$v_P=0$ at the extreme position, where displacement of particle is equal to amplitude.
i.e $y=\pm A$
Now the total energy of particle is,
$\text{P.E}+\text{K.E}=\text{T.E}$
$\Rightarrow \text{P.E}$ of vibrating particle will be maximum at extreme position, where $\text{K.E}$ is minimum.
$\therefore$ option $\left(c\right)$ is correct.