Question

The maximum acceleration of a particle in a sinusoidal wave is (symbols have their usual meaning)

• A. A${\omega }^2$
• B. A$\omega$
• C. A${\omega }^3$
• D. A${\omega }^4$

Answer 1

The correct option is A A${\omega }^2$

The wave equation of a sinusoidal wave is y(x,t) = Asin(kx-$\omega$t).
By double derivating this equation w.r.t. time we get the equation of acceleration.
i.e. a(x,t) = -A${\omega }^2$sin(kx-$\omega$t)
The maximum value of a(x,t) exists when the value of sin(kx-$\omega$t) is -1.
Hence, the maximum value of acceleration a particle can have is A${\omega }^2$.