Question

The maximum speed of a particle o a trailing wave is $v_0$, then find the speed of a particle wen the displacement is half of the maximum value

• A. $\frac{v_0}{2}$
• B. $\frac{{\sqrt{3}}_{V_0}}{2}$
• C. $\frac{\sqrt{3}{v}_0}{4}$
• D. $v_0$

Answer 1

Answer: (B)

$\frac{{\sqrt{3}}_{V_0}}{2}$

Speed of the particle,

$v=\omega \sqrt{A^2-x^2}$. . . . . . . . . .(1)

Maximum, $v_0=A\omega$. . . . . . . .(2)

At $x=\frac{A}{2}$

$v=\omega \sqrt{A^2-\frac{A^2}{4}}$

$v=\frac{\sqrt{3}}{2}\omega A$

$v=\frac{\sqrt{3}}{2}{v}_0$

The correct option is B.