Question

A sinusoidal wave propagates along a string. In figure (a) and (b). 'y' represents displacement of particle from the mean position. 'x' & 't' have usual meanings. Find : maximum velocity and maximum acceleration of the particles

• A. $\frac{3\pi }{2}mm/s,\frac{3{\pi }^2}{4}mm/s^2$
• B. $\frac{5\pi }{2}mm/s,\frac{5{\pi }^2}{4}mm/s^2$
• C. $\frac{7\pi }{2}mm/s,\frac{3{\pi }^2}{4}mm/s^2$
• D. $\frac{2\pi }{3}mm/s,\frac{3{\pi }^2}{4}mm/s^2$

Answer 1

The correct option is A $\frac{3\pi }{2}mm/s,\frac{3{\pi }^2}{4}mm/s^2$

From above figures, $T=4s$ and maximum amplitude $A=3mm$

$\therefore$ Maximum velocity, $V_{max}=wA=\frac{2\pi A}{T}=\frac{\left(2\pi \right)\left(3\right)}{4}=\frac{3\pi }{2}$ $mm/s$

Maximum acceleration, $|a_{max}|=w^{2}A=\frac{4{\pi }^{2}A}{T^2}=\frac{\left(4{\pi }^2\right)\left(3\right)}{4^2}=\frac{3{\pi }^2}{4}$ $mm/s^2$