Question

Fill in the blank
A travelling wave has frequency $v$ and the particle displacement amplitude $A$. For the wave the particle velocity amplitude is . and the particle acceleration amplitude is ..................

Answer 1

$x=A\sin (2\pi ft+\theta )$

$\Rightarrow \frac{dx}{dt}=2\pi fA\cos (2\pi ft+\theta )$

$\Rightarrow v=2\pi fA\cos (2\pi ft+\theta )$ ................(1)

$\Rightarrow \frac{d^{2}x}{d{t}^2}=4{\pi }^2{f}^{2}A\sin (2\pi ft+\theta )=a$

$v_{max}=2\pi fA$

$a_{max}=4{\pi }^2{f}^{2}A$