Question

Travelling wave has frequency $f$ and particle displacement amplitude $A$. The particle velocity amplitude and particle acceleration amplitude are respectively

• A. $fA$ & $f^{2}A$
• B. $2\pi fA$ and $4{\pi }^2{f}^{2}A$
• C. $A$ & $A$
• D. cannot be found

Answer 1

The correct option is B $2\pi fA$ and $4{\pi }^2{f}^{2}A$

Equation of wave is $y=A\sin \omega (t-x/v)$
Particle velocity, $v=\frac{dy}{dt}$
$=\omega A\cos \omega (t-\frac{x}{v})$
$\Rightarrow |v|=\omega A$$=2\pi fA$

Particle acceleration, $a=\frac{d^{2}y}{d{t}^2}=-{\omega }^{2}A\sin \omega (t-\frac{x}{v})$

$\Rightarrow |a|={\omega }^{2}A$$=(2\pi f{)}^{2}A$$=4{\pi }^2{f}^{2}A$